yeah in America there's 10M millioniares. That's 3.33% of the population. If you save your money not becoming a millionaire is impossible unless you are 50 yrsold, or have an IQ below ~90ish probably
TRUE..the repairman was looking to see if there were males in the household or someone else who might know he was gouging you when he did the repairs and billed you. i know LOTS of trades repair companies (especially plumbers and heater/AC) that permit their installers to keep half of the take. their crooked tradesmen will look around to gauge the ability of the customer to call BS on unnecessary or bogus repairs...especially on women who are unlikely to know if there even is such a thing as a conibbler pin or a fragistat. years ago my wife got a bid for $750 for new brake pads on a small car. when i called the guy to ask if that included the rears and new rotors and bearing he said no...JUST PADS, front only...no fluid bleed, no bearing regrease, not even a rotor resurfacing. i told him he should be ashamed of himself as i had a bid from the local legit repair shop for $130 including surfacing, repair persons are incentivized to overcharge but are smart enough to do it so they don't get caught
Think like me who doesn't fall in love to you, but who never allow you to be in love with anybody... Vs Think like I still sense some emotional gamblers trying to snatching you from me
Very enjoyable and clearly presented. Good to be reminded of how quick to jump to conclusions my mind can be, without taking into account the "background" info. Thanks much.
It's more important now than ever before that we ALL re-evaluate how we think and (more importantly) come to conclusions. Well presented and very thought-provoking. Thank You.
Good. I've "known" Bayes' rule for 50 years but your explanation was the best visual one I've seen. I like the way you apply it to everyday life. Thank you.
I wanna know wtf the repairman was doing because I peek around a lot and i dont have a lot of social experience, so i like to know what things people are doing wrong
@AmazingRebel23 A possible solution could be that he has never been in this place before and is trying to orientate himself, or is looking for potential threats as some people don't keep pets in a secure location when strangers come over. It also possible, just like you, the repairman is curious about their surroundings
Turns out Tom had just robbed the uni cafeteria, the repairman was hoping to catch a glimpse of ladies undies, and Bob was trying to alienate Alice before manipulating her into drink driving into a bridge
As someone who uses Bayesian systems professionally, in daily life thinking, and also to show why other people's arguments don't land, I have to say that this is a fantastic video. It very clearly illustrates to the layperson why Bayes is what is and what the messages are. I will be sharing this with others.
Let me guess, you're one of those geniuses that predicted that there was no way for Donald Trump to win? because after all, Hillary got the women vote, the latino vote...lol
I've often seen Bayesian analysis in the title of academic papers, and this explained the basic principle. But instead of offering five very similar examples, perhaps she could have moved on to some more advanced applications in scientific inquiry and statistics.
_"As someone who uses Bayesian systems professionally"_ It's funny, because for people with any amount of intelligence these kinds of methods would just be completely intuitive, obvious or logical when working out decisions, it's incredibly basic mathematics. But then I guess I should never be surprised by how low the bar can be.
+jamma246 If you think this sort of thinking is intuitive, then you might want to check out LessWrong.com so you can see how deep the rabbit hole goes. Fallacious and biased reasoning is the norm in 98% of the population. Most humans are extremely weak at rationality by default. This makes the world a rather frustrating place.
Four years since I first watched this video and for some reason, it is #1 on my recommendations today. Much appreciation. Watching this is bringing back fond memories of a summer long gone.
woah, that's SO strange because the same happened to me! I got recommended this video and the thumbnail gave me de ja vu, because I've seen it before. And I think it was four years ago as well.
This is really well done and appropriate for understanding the intuition of Bayesian probabilistic thinking. I teach this law to my Math students in grade 12 and I will show this video to them.
I realize I've been using this intuitively for years to fight my, or others' fears. But being able to quantify and codeify it is such work work of brilliance, I'm astounded. That's a smart person.
The trouble with updating beliefs while encountering new evidence today is we can all find evidence to support any belief. It really depends where one looks for said evidence. We all have so many information sources to tap now. So everyone can easily find whatever echo chamber they need, to reinforce whatever belief they hold dear.
Your statement is fully correct. It looks that statistics become more stable if you get more and more data. However the quality of data matters a lot too! And this is also included to the Bayes theory! The simplest example is having two Gaussian distributions, if you put them together, the tighter one will win, i.e. the more uncertain one has little impact. Indeed it is hard to quantify everything, but with the Bayes theory all is combined at least in a consistent way. If you want to get on something, the theory helps you not to loose.
Yes, you have to be honestly self aware to be able to use the principle - ie you have to ask the question "how would the data look in my personal echo chamber if I was wrong" vs "how would the data look in my personal echo chamber if I was right"? And you would honestly have to draw the conclusion that my echo chamber will still only resound the message I already have taken as true, wether my belief is true or not.
You have to be able to weigh the quality of the evidence to the best of your ability and be honest with yourself of how good you are as a judge that evidence. Intelligent people tend to be realistic of their limitations while unintelligent people are overconfident - Dunning Kruger and all that.
Well said - this leads to a-priori vs a-posteriori and the implementations of mankind's laws compared to the laws that persist before mankind. The reduction of our illusions to the essence of what they are derived reveals more than most are willing to admit. That means change in the face of the ego's desire to remain inflexible. The forces that drive the game are that of care and desire and they are inescapably bound in this place. You will always desire something. You will always care to reveal the desire's outcome. To actually escape this issue is = _____ fill in the blank.
I've done a lot of repair work, and I know what's it's like to be in the category: "looks like he's going to rob you but really he's just doing his job." Let me tell you - every place is built differently, and you should always keep your eyes open.. One time I found a gas line going into a bedroom and not even capped off. The place would have filled up with explosives at the turn of a knob, well if not for my "snooping about" that is. But it's also part of the job description to not freak people out. I just said, "I need to look around a bit to make sure I know where all the gas lines are going."
That girl did not provide adequate background on stove repair. Like, old house, gas or electic stove. Why is this critical information? A good repair-man/woman, would look around to not only fix the point but also all connected to that point. Also, it would be so easy to inquire, why are you looking into bedroom/s? She phrases it snooping, which is secretly done, which did not seem to the situation/
As a repairman also, I'll throw in my 2 cents worth. When you enter a house to do repairs you should always examine your surroundings to identify any potential exit points or hidden dangers such as friendly dogs that don't bite (been bitten twice).
Brew Sauce+ I've done a lot of electrical repair work, and it becomes second nature when entering an unfamiliar place to glance around looking for potential problems, to a point where one may not even be aware of it. And btw, I've spotted many problems -- shock and/or fire hazards -- that the homeowner was oblivious to. It is the responsibility of the electrician to spot these hazards, point them out, and recommend (even insist) appropriate remedies. I imagine it's the same for someone coming to repair your gas range (assuming it is a gas range). He would want to know if there any other gas appliances in the house, any lines/valves/couplings that might be problem, etc. It would be irresponsible to not ascertain this info.
Bayes' Rule is an important component of critical thinking. The ability to think critically is a skill that needs to be learned. The challenge is that common sense and intuition are often very wrong, and there's no trivial way for knowing when. It's on a case-by-case basis, and all those cases are about patterns that need to be recognized and examined.
Repairman snooping around for the circuit breaker: Appliance repairmen sometimes have this weird preoccupation with turning off the electricity to an appliance before they work on it. 220 volts can really ruin your day.
In the UK at least, by law there has to be a circuit breaker within reach of the stove. In the US it will be split phase, so pretty hard to get the full 220v.
These personal experience examples were amazing, helped understand it more intuitively. Thank you! Came here after crunching through some equations but these real world examples showcased the theorem in a very simple way.
This is REALLY GREAT. I frequently come across content about how everyone is illogical that go on to provide examples of things i would NEVER do. These mistakes that you are teaching to guard against, however, are ones I know i do fall victim to and thus need to vigilantly guard against And you do a good job providing practical ways to guard against them If only i knew more people whose difficulties with logic, consistency and constantly affirming their pre-existing narrative weren't caused by far more basic deficiencies - usually deficiencies in CHARACTER at least as much as logic itself
The fact that there's so many comments here along the lines of "wow, this totally changed my perspective on everything" is quite unsettling to be honest.
The willingness or openness to challenge your initial impressions, and subsequently alter them, is a component of the attribute we used to call "humility". It has more to do with wanting to see things accurately, than it does with some false sense of being humble.
_sees repairman checking out my bedroom_ _slams him against the wall_ "8% chance you're gonna rob the place, huh punk?" "but sir, I'm here to repair your bed" "Bayes would disagree .... get out before I call the police"
Your videos have added that extra weight to my priors I need to convince me of the merit of Bayes Theorem. I'm committing myself to practice Bayes thinking. Thank you!
@@gyrojomo Your perspective is of equal relevance to me, a 3rd party stranger. And perhaps OP's statement can nudge one more person into accepting the rationally sound choice of incorporating Bayes Theorem into their lives. That is a non-trivial post, but yours seems negatively intended and leaves me wondering, for what purpose?
@@gyrojomo dude. I don't want to assume you meant to be rude, so you should really work on how you relate to other people. That was painfully awkward to watch.
I never update my priors. In fact I would have assumed the repairman was wondering where he was gonna lay me out after eating my liver with some fava beans and a nice chianti. Fake repairman is the oldest cannibal trick in the book.
Couldn't help smiling when I head the words 'Berkley' and 'snowflake' in the video. Hard to imagine extremely intelligent people becoming snowflakes. But may be there is no correlation between intelligence and wisdom. Not saying the presenter is a snowflake. But I see a lot of young people take positions that would be considered 'progressive' in their eagerness to 'look' elite among their peers.
+B-Rad that's exactly what I am talking about - Classic elitism. I should have also added that this behavior has to do with conforming with 'views' spread by the progressives elites, so one could look like them. It is implied in my statement, but seems some people need more clarification. Let me guess, you 'think' to care about animals & environment means to not eat them, because you have 'learned' this info from material that you read or watched on T.V or the internet. If you tell me you have a psychological problem to kill and eat another living, breathing thing, I will probably excuse you. But, the loving animals and earth etc is baloney. You just don't realize it is baloney - that's all. If I prove to you that vegetables and plants also perceive pain..... my bad, this has already been proven. (Read about scientist Bose's work from more than a 100 years ago) Will you stop eating food altogether?
As to the final part, "Update incrementally", it is good to keep in mind when doing so that forming a general principle based on personal exposure, even if to many adherents, is still anecdotal not empirical, and thus influenced by the persons own biases or the context of the social norms. So in Berkley, where there is a lot of new-agey sentiment there are more people who feel that meditation is beneficial and this in and of itself can increase ones own personal perception of benefits, or if formulating opinions based on informal tallies of personal interactions, lead you to think, well it must actually have positive benefits because so many of those I encounter say it does. It is much like if you went to Brigham Young you would find many more people who said that prayer caused changes in the world or if you were at a Rainbow Gathering you would find a high percentage of people who felt LSD expanded your mental abilities and capacities.
Well said! That incremental exposure to an idea is how advertising works. One would be better off to let the positive words from a respected friend lead them to research the scientific evidence of the changes that, in this case, meditation makes in the brain as shown in brain imaging/scanning.. Excellent video. Really makes the theory understandable.
Another important clue that Tom is a Math PhD student: He's walking. MBA students travel around campus in golf carts that they stole from the campus maintenance department.
remember your priors, how likely is it that a math PhD has the courage to venture outside of their room and into the savage social environment of the campus
Problem #1: When an accident happens, what is the probability that the accident is caused by a bad driver, given that: 1) 90% of the population has been involved in at least one accident 2) 30% of the population are bad drivers (means 70% are good drivers) 3) 99% of the bad drivers are involved in at least one accident P(Bad Driver) = 0.3 p(Accident|Bad Driver) = probability of a bad driver causing an accident = 0.99 P(Accident) = 0.9 P(Bad Driver|Accident) = probability of an accident caused by a bad driver = 0.99 * 0.3 / 0.9 = 0.33 = 33% When an accident happens, there is only 33% chance that the accident is caused by a bad driver. --------------------------------------------------------------------------------------------------------------------------------------------- Problem #2: Find the chance of having cancer, given that the customer is 65 years old. Facts: (a) 1% of the population have cancer (99% don't have cancer) (b) 0.2% of the population is 65 years old (c) Of those that have cancer, 0.5% of them are 65 years old P(Cancer) = 0.01 P(65 yr old) = 0.002 P(65 yr old | Cancer) = 0.005 P(Cancer | 65 yr old) = What percent of the 65 year old population is likely to have cancer = P (65 yr old | Cancer ) * P (Cancer) / P(65 yr old) = 0.005 * 0.01 /0.002 = 0.025 Only 2.5% of the 65 year old population is likely to have cancer. --------------------------------------------------------------------------------------------------------------------------------------------- Problem #3: Given the following: (a) 1% of the population have breast cancer (99% don't) (b) 80% of the mammograms detect breast cancer (20% don't) (c) 9.6% of the mammograms detect breast cancer when it's not there (90.4% of the tests correctly return a negative result). You have got a positive result.What are the chances that you have breast cancer? P(Breast Cancer|Positive Result) is what we have to find. P(Breast Cancer) = 0.01 P(Positive Result|Breast Cancer) = 0.8 P(Positive Result) = We need to consider both positive and false positive = Positive + False Positive = You have breast cancer and you have been correctly identified as having breast cancer + You don't have breast cancer but have been identified as having breast cancer = 0.01 * 0.8 + 0.99 * 0.096 = 0.10304 P(Breast Cancer|Positive Result) = 0.8 * 0.01 / 0.10304 = 0.0776 So, if you have a positive result, there is only 7.76% that you have breast cancer.
Problem #4: Spam detection (a) 50% of the emails are spam (b) Out of 1000 spam emails, 110 contain the word 'Nigeria' (c) Out of 1000 non spam emails, 48 contain the word 'Nigeria' A message with the word 'Nigeria' arrives in your inbox. What are the chances that this message is spam? P(Spam|Nigeria) is what we have to find. P(Spam) = 0.5 P(Nigeria|Spam) = 0.11 P(Nigeria) = Probability of a message having the word 'Nigeria' = Probability of word 'Nigeria' appearing in a spam email + Probability of 'Nigeria' appearing in an non spam email = 0.11 * 0.5 + 0.048 * 0.5 = 0.079 P(Spam|Nigeria) = P(Nigeria|Spam) * P(Spam) / P(Nigeria) = 0.11 * 0.5 / 0.079 = 0.69620 There is a 69.2% chance that the message containing 'Nigeria' is a spam.
xazzbi Yes, just draw the rectangles as in the video. Instead of Math/Business you have cancer/no cancer, and instead of shy you have "positive result".
P(Cancer) * P(65 yr old | Cancer ) represents the Probability that someone you know nothing about has cancer AND is 65 years old (first you take P(Cancer) since you know nothing about that person and then you multiply P(65 | cancer) since the cancer part is already included in the first probability). Now you have the "pool" of people who are both. But since you know (in the problem) that the relevant portion is 65 years old you have to divide by that probability to include that knowledge. Proof (I know it's not helping to visualize :P): P(Cancer) * P(65 | Cancer) = P(65&Cancer) = P(65) * P(Cancer | 65) P(Cancer | 65) = P(65&Cancer)/P(65) = P(Cancer) * P(65 | Cancer) / P(65)
It should be noted that the conclusion of problem #3 only applies if you randomly test people from the population. If you were prescribed a mammogram to begin with, there are other reasons why your physician suspects you might have cancer, and therefore belong to a population that, even before testing, has a chance of having cancer higher than 1%. Also, is your figure of 9.6% of false positives a real one or did you make it up?
I couldn't help being distracted by that light switch just left of your head, so . . . Bayesian thinking: 1. By your accent, you are probably American filming this in the USA. 2. Common US building code makes the top of the light switch about 4' high. 3. By making a quick judgement call, if you were standing up for this video your height would be about four foot, three inches. 4. By my experience the percent of adult women in the US who are only that tall is less than 1%. 5. I am adjusting my perception of you standing in front of a wall to perceiving you seated in a normal chair talking to a camera on a tripod. Okay, I am subscribing to your channel.
This reminds me of a Government ad I used to hear on the need to wear seatbelts. It basically said you need to wear your seatbelt even on short trips close to home because something over 50% of all accidents happen within 5 miles of home. And, well, duh. 99% of all miles traveled in cars is within 5 miles of home. Anyway, 87.32% of all statistics are made up on the spot.
I think it makes sense though, if people are not wearing their seat belt because they think that since it's just a short trip they don't need to. So, it is countering an inappropriate instinct. Because maybe people don't think about the cumulative distance they are travelling in short trips.
In 2002, Angela Cannings of Salisbury in the UK was convicted of murder in the death of her second and third children, apparent victims of Sudden Infant Death Syndrome (SIDS). The prosecution argued that the probability of a single instance of SIDS is 0.004% and therefore probability of a second instance is so small that homicide is the only likely explanation. The conviction was overturned on appeal when a statistician testified that, while the probability of two SIDS deaths in one family was vanishingly small, the probability of two infanticides by a healthy middle-class mother was actually much smaller. This is what can happen when you don't remember your priors!
Jim McDonald that’s not what happened at all. The problem was with the assumption that sudden infant death syndrome events in a family are independent events. The expert witness in the first trial believed this. But on appeal they found a different expert witness that showed they are not independent events and that sudden infant death syndrome has been shown to be influenced by inherited genes. It wasn’t overturned because the probability was indeed vanishingly small but double infanticide less so, it’s the fact that it isn’t vanishingly small at all!
A better example is the early use of DNA evidence. Probabilities of marker matches were given as if the suspect were randomly chosen from the entire population the DNA database was based on (naive frequentist). Of course, the actual pool of plausible suspects was normally limited to people in a single community or sometimes even a single family, where the probability of sharing particular markers can be quite different. Gets even worse when talking about multiple markers and their joint probabilities. There are details I'm leaving out, but that is the very general idea. This was all put in frequency language, but it blindingly obvious if you just use a Bayesian framing. My PhD adviser (population genetics) actually testified in court as an expert witness against DNA evidence in some of those early cases; then turned around and testified in support of DNA evidence (including some Innocence Project stuff) once the FBI got their shit together on the statistics.
All this proves is that our society is incredibly gynocentric and women are allowed to get away with murder. The UK is known for being REALLY bad about this. I wonder what they did if she killed a 3rd later on: www.telegraph.co.uk/news/2017/05/16/oxford-student-spared-jail-extraordinary-talent/
Also, no statistician "proved" that the probability of 2 infanticides by a middle class mother is much smaller. If she kills once, she's FAR more likely to kill again than a RANDOM OTHER female member of the population. I don't believe for a MOMENT that this was legitimate math. This is gynocentrism. The pussy pass.
I would also imagine that multiple incidences of SIDS occuring in proximity wouldn't be a true statistical anomaly since the deaths could have been caused by the same factors.
I didn’t know this had a name. I thought it was simply being curious and not judging a book by its cover. I’m glad it resonates with people and I hope they’ll adopt it and apply it to everything happening these days. Because these days people think they’ve read the book because somebody on social media recommended it to them.
I've always liked to use something close to this general thought to keep my analysis, general guesses and knowledge of stuff updated and changing, avoiding fixed preconceptions or prejudices. This is quite similar in many ways to my personal system, although I haven't put it down in numbers or created clear rules and patterns, it was more psychological and simple. It's very interesting to find something close, and makes me even more interested in the possibility of studying statistics, something I already like a lot, but don't know if I like enough to live on it. Thanks for this, I think I first saw you with Matt Parker on Bayes. Keep up the great job. Every detail can have a small influence on coming to momentary (?) conclusions, always doubt yourself.
I don't know much about meditation, but as far as I do know, meditation is nothing more than you practicing to control your racing thoughts. And as we all may know, the more you practice something, the better you get at it.
@Fernando Cunha I'd actually say that it is incredibly simple once you get the hang of it. What could be simpler than winding down? I've done it for 10 years and I love it. I'd also just say that it is more about being attentive and open to yourself than about actually wanting to controlling your thoughts, though it's true they will become calmer and more focused. I would agree however, that without some practice in a meditation centre under a proper teacher it can be difficult to get the hang of it by yourself. I highly recommend the books and talks (a lot of them are in youtube) by Thich Nhat Hanh (vietnamese zen master). He speaks plainly and powerfully, in a way akin to science. He likens zen theory to Lavoisier's principle of the conservation of mass. And you can feel that he is largely free from attachment and dogma.
This is great, particularly the animation of updating your priors after receiving new information like in the meditation example. Most people only update their priors when they get a result that confirms their previous bias.
I reluctantly agree. And I perceive that social media, with its stovepiping algorithms, exacerbates this. One can, almost without noticing, end up in silos where there is a high degree of conformity of opinion, and where differing views are subtly, or not so subtly, marginalized. In my own case...though I try to avoid confirmation bias, I have no doubt that I'm afflicted with it. It's easy, maybe even comforting, to be surrounded by people who agree with you, and to latch on to tidbits of info that confirm one's vested position. OTOH, when I re-think a position, based on new evidence, or even a compelling personal testimony or someone eloquently putting forth a different view, it feels liberating.
I had the same thought when she mentioned meditation. How can sitting down and doing nothing be 'fake'? More like 'I dont have what it takes to do it, so I'm gonna call it fake to convince myself it doesn't work'
Why would you like something that encourages falsity and error? Are your feelings more important than discerning the truth (which is the basis for this whole video)?
I've been struggling to "get" bayesian stats for a couple of years, sorry to say, because even in my technical work (biomedical informatics) I need visual representations of abstract relationships to help me think through problems. So your visual aids were extremely helpful to me. They took a rather wobbly abstract concept of priors and offloaded them to a visual concrete representation to reduce cognitive load. Thanks so much and I've subscribed to see what else I can learn!
To me, it's a cognitive load even after visual representations. One is either numerically/scientifically predisposed or isn't. I don't think you can force yourself to become adept at something you're not naturally adept at.
Thank you for this video. I really like how you show that mathematical thinking can improve your life. I do have one quibble and that is that it doesn't seem like you are applying Bayes' Rule, it seems like you are applying conditional probability. As I understand it, Bayes' rule shows the relationship between P(A|B) and P(B|A). If I knew the probability of someone being shy if they were a math student, and wanted to know the probability of them being a math student if I had prior knowledge they were shy, that would be an application of Bayes' rule. Conditional probability is a concept that predates Bayes' rule. I may be missing something which you can explain, but in any case thank you for the fine video.
This is a really good explanation. The weakness of Bayes is hidden in Julia’s explanation, though. Namely, so often the probabilities aren’t really probabilities but just numbers that people make up. This can lead to a sort of confirmation bias. A fairly easy example of this is the question of whether humans are the only life forms in the universe. There is currently only one example of life, so we really don’t know how likely life is given some set of priors. People who think there is something special about Earth will give a completely different number to someone who doesn’t. Consequently, two people using Bayes to ask the same question get totally different results and coincidentally (not) they get the answer that supports their preexisting belief. This isn’t meant to say that Bayes is useless. It’s not. We just need to be aware of where we are using real numbers (students in a PhD program) versus made up numbers (how likely someone would diagnose a business major of being shy).
Bayesian stuff is all about updating the 'posterior probability'. As new info is gained one adjusts the priors and get more accurate probability determination. So one could start with total unknown prior of 50% and still get useful Bayesian results. Note: my current understanding of this. Actual Bayesian application in real situations is very complex. A good book is 'The Book of Why; The new science of cause and effect.' by Judea Pearl
Corresct: We just need to be aware of where we are using real numbers (students in a PhD program) versus made up numbers (tentatives to fix the probability os inteligence life)
Hi, Julia. I just stumbled on your channel. Thanks for this! And an observation: I'm struck by how similar Bayes's style of thinking is to David Hume's. I imagine there's some already well known connection here.
Meditation is real, the mind is a real rabbithole. I accidently stumbled upon a type of walking meditation. It shifted my mood and how I prioritize things for a few weeks. I was very productive, the effect was acute and obviously to me had began after the meditation experience. But I was unable to reproduce it.
i believe you! ....that is because you can only move forward to the next level of meditation and can never remanufacture a previous season of it as it is a spontaneous newfound prayer which is nestled between two eternities which shall never occur again! we go from faith to faith and from glory to glory! Eventually, if one continues in meditation to its supernatural end, you graduate from meditation into contemplation, which is effortless perpetual spiritual prayer without the use of the natural carnal intellect!
Think more to not be fool either by how others testedly testing my way of knowledge perceiving life... Vs Think more just like I know what my hands did in an hour, a day, a week, a month, a year and how I bestowed on the outcome of it regularly
I used to dismiss the word "intuition" the way you used to dismiss "meditation". The way I heard it often used was like a person were saying, "I'm making this claim without any evidence at all, based on my emotions, and any challenge will be deemed hostile". The implication is only a little exaggerated there, but you've likely heard "intuition" used as frivolously. Eventually, though, I heard someone discuss a subconscious thought process -- the idea that the brain is recognizing patterns seen before. Example: Mom tells teenage daughter the new boyfriend is no good for the daughter. The subconscious part is that the mother has seen males with similar behaviors and speech, and those males were no good, the "love 'em and leave 'em" type, for example. While Mom may not know what details mattered, the subconscious triggered anyway. So while some folks still might toss around "intuition" carelessly, for others, there is probably something to it.
Agreed on the theory you described of how "intuition" is built. It's a sub-conscious pattern recognition process. The big problem with intuition is, that it is anecdotal and completely depends on your own life experience. In your example: What if mom, had only met an outlier group of males for which the behavior seen indicated they are bad as a partner (but hasn't been exposed to the normal population of males that exhibit the behavior but are good partners?) This is obviously possible, but the intuition mom built, based on her sample would be completely wrong... Intuition is not bad per se, it's essentially a short cut that can save us from analysis paralysis, but it can go off the rails very quickly...
Intuition is really just picking up small details unconsciously, you put them together later and come to a conclusion. I'm no mathematician, but a lot of what she's saying is part of normal thinking, and no doubt contributes to what we call intuition.
more like consider likelihood of event happening due to volume/sample size. If sick person vomits 5/10. If healthy person vomits 0.5/10. There are 4 million healthy people. There are 1000 unhealthy people. So, 200000 healthy people are vomiting. 500 unhealthy people are vomiting. A person vomits. He has 1:400 chance he is sick, vs 400:1 he is healthy. 400 x more chance.
The issue with this that I can find is that, in these examples, you're still pulling percentages and ratios out of thin air. Now granted, you're trying to correct an assumption on the fly. But correcting an assumption based on more assumptions, you can still be wrong with your initial set of assumption. For instance, maybe repair men aren't more honest than not. Maybe thieves are very common among st repair men in your particular neighborhood?
Those would be included in the prior. P(he is a thief | he looked like he was snooping) = P(he looks like he is snooping | he is a thief) * P(he is a thief) / P(he looks like he is snooping). Your priors have your estimate of P(he looks like he is snooping), P(he is a thief), and P(he looks like he is snooping | he is a thief), however it is that you came up with these quantities. All the things you described are just things that could be taken into account when your priors are determined
couldn't it be partially remedied with exaggeration and underestimate aka considering the best/worse case scenario? that's a super high percentage for shy math students (75%) and super low percentage for shy business students (15%)
I look at new information on whether it's persuasive. I used to work in legal research. If I was right with the proper rule and information my idea was unshakable and irrefutable. Other times I had to concede I was wrong and I knew exactly why I was wrong. I always learned something new.
Minor point, but... when it comes to mental health, a consistent placebo effect is better known as a "cure". If something makes someone happier regularly, calling it a placebo effect is kind of meaningless, no?
maybe in the realm of mental health, it could mean that it might seem to be working to cure their mental issues, but is actually only demonstrating short term cures and nothing permanent or in the long term. Depends on what the context and goal is though, I guess.
I like her thinking. Reminds me of little Johnny in class. The female teacher hides a fruit she gets out of a bag behind her back and says, “Class, I am holding a fruit behind my back. It’s long and it’s yellow. Who can guess what it is”? Little Susie holds up her hand, then the teacher calls upon her, and she says, “it’s a squash”. The teacher displays the hidden fruit and says, “No Susie, it’s a banana. But I like the way you’re thinking”. The teacher then secrets another fruit from her bag, hides it behind her back, and says to the class, “I am holding a fruit behind my back. It’s round and it’s red. Who can guess what it is”? Little Mikey holds up his hand. The teacher calls upon him and he says, “It’s a cherry”. The teacher then displays the hidden fruit and says, “No Mikey it’s an apple. But I like the way you’re thinking”. Little Johnny then asks if he can hide something. The teacher thinks for a second and says yes. So Little Johnny puts one hand in his pocket and says, “ Teacher, I’m holding something in my hand. It’s round and it’s hard. Can you guess what it is”? The teacher blushes bright red, then becomes enraged, and says “Little Johnny, we will not have any such vulgarity in my class. Go to the principal’s office right now.” Little Johnny then displays what he was holding to the class and says, “Teacher, it’s a quarter. But I like the way you’re thinking.”
@@rephaelreyes8552 Yeah that's why mathematicians have all the private jets, super cars, and hundred foot yachts, and they get aaaaalllllllll the bitches. LOL shut the fuck up.
There is scientific studies about how meditation works. But there is a basic logic on meditation, a person who takes some time every day to just stop everything and stay calm with the eyes semi-closed and try to keep his mind calm and open for a period of time... if he/she do it periodically then of course his brain and nervous system will work in a different way than a person who never trains to be calm and is always overload with emotions. I do not understand why somebody would think that "meditation is Fake". The mere sentence doesn't even make sense, you could think that meditation doesn't produce results, but the act of meditation itself is not fake, even if it didn't work, you did it and "wasted your time". Also this means that meditation is poorly understood by people who don't know about it, often they think it has something to do with superstitious phenomena, when instead, meditation is just what the word implies: thinking deeply. There is different types of meditations: for instance watching your video is a meditation, specifically an Analytic Meditation. There is also abstract meditations, but I'm sure you get the point, if you spend some time with no physical activity whatsoever, no external supporting tools, only using mental tools to make your mind work in either an abstract or analytic way, then your mind will evolve, and even physically your brain will adapt to that kind of training and improve (if your meditation is aimed in the right direction, of course) because as you may know, the brain's cells ability to re-order and create new synapses is quite remarkable, so this should give us a clue to why meditation works. Look at how the odds are low for meditation not "being real" that even if it was a "placebo" you missed the point that a placebo is a result of the mind thinking something is helping so the results shows it is working... THE MIND, a placebo is one of the features of the mind influencing the whole nervous system and the body (and that is a tool of meditation). As you may see, that square is still not drawn in the right way, even after you corrected it... I am sorry your video is great, you are amazing... I think that's why it really destroyed me that initially you thought "meditation is fake".
Calling it fake may be a lazy/overly-broad way of saying that mediation is so poorly defined, on top of being a subjective self-reporting, that it's tough (impossible) to find any reason to believe it can be definitively found to be efficacious. Consider cognitive behavioral therapy (CBT) and its successful track record. Is CBT a set or subset of meditation or vice-versa. Do they need to be teased apart? CBT involves exceptional concentration via structured introspection. That act overlaps with things that take place while engaging in various forms of meditation. But it doesn't require focusing on breath, or finding your center or any other aspects. So telling someone that a bit of structured concentration can do wonders for you is as valid as saying meditation works. It shouldn't come as a surprise that active management of your mental dialogue (including 'clearing your mind') can yield positive results.
Well said, Eagle Dee. They might be more "in control" of their emotions and less likely to be bouncing between addictions or merely reacting to stuff. Maybe they over eat less.
How do you assign probabilities to something like "meditation works?" There is no definition of what constitutes achieving a meditative state, and no precise goal of self-improvement that might be fostered by the practice. Coherent terms matter. Also, the assumption that one's "priors" were, themselves, correct is questionable. I'm not saying the Bayesian principle isn't useful; you just have to remember its limitations.
With that example, in particular, the priors got "updated" based on new information. The priors are seemingly arbitrary but it is important to keep in mind that they can (and should) change based on new evidence. It's important to be aware of priors when making assumptions about observed events, as it is far too easy to make a number of logical fallacies otherwise.
You do indeed have to be aware of priors when making assumptions; I think the point I was trying to make is that assumptions underlie one's assessment of priors.
First you should obviously define for yourself what do you mean by "meditation works", what is it supposed to do if it is "working". In this case it seems that meditation is supposed to make you feel happier, and the question becomes, "does meditation make you feel happier?". And that can very much be evaluated, just ask people who started meditating if they feel happier after they started, that gives you at least some weak evidence. Now personally i think its quite sufficient to believe yourself to be happy in order to feel happy, healthy brain chemistry should take care of the rest. Given that only people who start out with belief "meditation makes you feel happier" are likely to actually try doing it, it becomes obvious how meditating can create belief that you are supposed to be happy followed by actually feeling happy. So on the surface, it would seem "meditation works", but no theory is much good if you don't try to falsify it, so how would you go about it. In case of my pet theory, one could gather a group of people who don't believe "meditation makes you feel happier" and convince them to try it anyway(for the sake of science/pay them to do it) and gauge their perceived happiness levels before and after. One can imagine the end result. Then perhaps you can add a caveat to "meditation makes you feel happier", "but only if you expect it to" and thus gain new understanding of how happiness actually works.
What Jan said. Both times. It very, very, very often trumps everything, regardless of how soundly the mathematics were applied. That is how for example the United States Congress passed a bill to increase the amount of Medical Care (and as a bonus, add administrative cost!), and actuarially state with a straight face the it would REDUCE overall costs!! This actually happened in the U.S. in 2009. "It's the assumptions, stupid!"
I didn't like the meditation and the jealous guy examples, because in those scenarios the probabilities are completely made up, and you only get a confirmation bias of what you already expected to be very probable. Bayesian can be very tricky...
You missed the entire point bud. Zoom out a bit. Those subjective examples are perfect _because_ they are not precisely defined and are ill-suited for "real" scientific study. The point of these examples is to illuminate Bayesian _thinking,_ which is different from _applying_ the Bayes' model to determine whether Bob is jealous or if meditation makes people happy. A real example with objective results would detract from this video's purpose because it would be easier to miss the point by getting caught up in, "Oh cool, meditation works," or, "Dang, so Bob WAS jealous. I knew it." With the examples in this video we instead see the process by which we might organize different factors and note changes in them; hell, even just noticing that there will be changes is stressed -- e.g. "update incrementally." The point of this video then was not _to_ conclude answers to _these _*_particular_* questions or problems, or even to demonstrate that these questions or problems can be answered or solved; the point of this video was _how_ to conclude answers _across a broad range of _*_possible_* questions or problems.
TurdFurgeson571 You did not consider another possibility, which is that her examples actually demonstrate why statistical reasoning is often misleading. To put it succinctly, probabilities do not prove causalities. On top of it, most mathematicians I know do not consider statistics to be a branch of mathematics. It is not difficult to find out why.
@@pawelpap9 I doubt that a video titled "... Bayesian thinking" is going to delve into the pitfalls. This seemed to me to be a broad overview. For her to go from this 30,000 foot view down to the more granular discussion of how stats must ultimately be interpreted, which opens us up to reading the data in a misleading way, seems like too big a leap for even the most novice content creators or script writers, so it just doesn't seem like the purpose of this video. Additionally, if that is her intention, she's being awfully coy about it, rather than just coming out and saying, "Be careful."
The jealous guy example worked well, because the point was she had a lot of evidence prior to believe he was jealous, therefore the area of the jealousy square was larger. I think you just misunderstood the point.
This is the kind of woman the media should be giving exposure to, and not the Kardashians of the world, if we start valuing the pursuit of knowledge, with acknowledgment, money, fame, etc the society will be a better place for all of us.
Was getting my first shot yesterday and feeling a little anxious and then looked around at all of the people around me and imagine the room being full of this many people constantly, every day for weeks and I hadn’t heard a single issue on the news in my city about any problems so that made me feel better. Funny thing, it doesn’t work for me on plane rides, though. I think about how there’s 5k+ flights every day in US and no accidents so what are the odds THIS one will be the one. Still doesn’t work for me. Still sure I’m going to die every time.
Thank you for this video. Your examples are super enlightening and I feel like you've communicated the idea of prior and posterior probability better than my own theory of probability/statistics classes. One thing I wanted to mention, though, is that I think we need to change the way we think about the term "placebo" (and I'm very guilty of this myself). You say that the placebo effect could be evidence that meditation is fake, but I'd argue that the placebo effect can also be evidence that meditation does work. If Bob expects meditation to work, and it results in him being happier, then the mechanism "behind" meditation ultimately doesn't matter because it works for him regardless. The same can be said for placebos in double blind medical trials. If a person sees benefit from taking a placebo, unaware that it's a placebo, that doesn't negate the fact that they saw benefit from it. Sure, the placebo isn't "doing" anything, and there are definitely other factors at play that could be helping, but our brains are also weird and easy to fool. Anxiety is strongly linked with gastrointestinal health, and psychosomatic symptoms are still symptoms. Just some food for thought!
If I see Tom I can see what Tom is wearing. That will ultimately narrow down one's guess. Given one or two more data points and you're well upon your way to knowing the specific kind of maths or business.
Think more the hardest way as wise as how I'm honest to myself, with every details of how I spend my precious seconds of every minutes of every hours.... Vs Think more the hardest way even when I was supposed to be happy in a framely set-up man-made time-line schedule
before video : chances of me being a millionaire 0.1%
after video : i applied bayesian thinking (remembered my priors) , now the chance is 0.0001%
What was the new piece of information you used to update your priors? I'd love to see the full calculation. ;)
Reality bites!
asdfghyter fact that he is wasting his time on UA-cam might be one of them :p
yeah in America there's 10M millioniares. That's 3.33% of the population. If you save your money not becoming a millionaire is impossible unless you are 50 yrsold, or have an IQ below ~90ish probably
Sudhamsu
You live to the ripe old age of 125 :)
If a repair man wants to rob you, he'll do it when he's writing the bill.
Good One!
TRUE..the repairman was looking to see if there were males in the household or someone else
who might know he was gouging you when he did the repairs and billed
you. i know LOTS of trades repair companies (especially plumbers and
heater/AC) that permit their installers to keep half of the take.
their crooked tradesmen will look around to gauge the ability of the
customer to call BS on unnecessary or bogus repairs...especially on
women who are unlikely to know if there even is such a thing as a
conibbler pin or a fragistat. years ago my wife got a bid for $750 for
new brake pads on a small car. when i called the guy to ask if that
included the rears and new rotors and bearing he said no...JUST PADS,
front only...no fluid bleed, no bearing regrease, not even a rotor
resurfacing. i told him he should be ashamed of himself as i had a bid
from the local legit repair shop for $130 including surfacing, repair
persons are incentivized to overcharge but are smart enough to do it so
they don't get caught
Mortimer Snead He likes the way you decorate?
VALID POINT !
You should tell your wife to have her Veyron serviced somewhere else.
I have absolute no idea why this was recommended to me but here’s a new subscriber.
If the algorithm recommended it, think of it as good fortune. If it was a friend's recommendation then maybe it was a hint to be more open minded?
Yep
Think like me who doesn't fall in love to you, but who never allow you to be in love with anybody...
Vs
Think like I still sense some emotional gamblers trying to snatching you from me
....
3yrs later-my myself included
....
Very enjoyable and clearly presented. Good to be reminded of how quick to jump to conclusions my mind can be, without taking into account the "background" info. Thanks much.
It's more important now than ever before that we ALL re-evaluate how we think and (more importantly) come to conclusions. Well presented and very thought-provoking. Thank You.
Good. I've "known" Bayes' rule for 50 years but your explanation was the best visual one I've seen. I like the way you apply it to everyday life. Thank you.
The fact that none of those stories were completed shakes me to my core.
I wanna know wtf the repairman was doing because I peek around a lot and i dont have a lot of social experience, so i like to know what things people are doing wrong
Ikr?
@AmazingRebel23 A possible solution could be that he has never been in this place before and is trying to orientate himself, or is looking for potential threats as some people don't keep pets in a secure location when strangers come over. It also possible, just like you, the repairman is curious about their surroundings
Probably looking for the breaker box or something.@@AmazingRebel23
Turns out Tom had just robbed the uni cafeteria, the repairman was hoping to catch a glimpse of ladies undies, and Bob was trying to alienate Alice before manipulating her into drink driving into a bridge
As a statistician, I have never looked at Bayes visually like that and considered it using area. Thank you for a new way of looking at this.
As someone who uses Bayesian systems professionally, in daily life thinking, and also to show why other people's arguments don't land, I have to say that this is a fantastic video. It very clearly illustrates to the layperson why Bayes is what is and what the messages are. I will be sharing this with others.
Let me guess, you're one of those geniuses that predicted that there was no way for Donald Trump to win? because after all, Hillary got the women vote, the latino vote...lol
Let me guess, you're one of those people that mocks people a lot and ends their sentences in...lol
I've often seen Bayesian analysis in the title of academic papers, and this explained the basic principle. But instead of offering five very similar examples, perhaps she could have moved on to some more advanced applications in scientific inquiry and statistics.
_"As someone who uses Bayesian systems professionally"_
It's funny, because for people with any amount of intelligence these kinds of methods would just be completely intuitive, obvious or logical when working out decisions, it's incredibly basic mathematics. But then I guess I should never be surprised by how low the bar can be.
+jamma246
If you think this sort of thinking is intuitive, then you might want to check out LessWrong.com so you can see how deep the rabbit hole goes. Fallacious and biased reasoning is the norm in 98% of the population. Most humans are extremely weak at rationality by default. This makes the world a rather frustrating place.
Most people are really good at "Biasian" thinking.
genius pun ... duh
I see what you did there.
...which is to say, really good at fear mongering and mystical belief.
But they have to weigh up how true it is first.
bahaha i love puns. really helps that its spelled out lol
Four years since I first watched this video and for some reason, it is #1 on my recommendations today. Much appreciation. Watching this is bringing back fond memories of a summer long gone.
woah, that's SO strange because the same happened to me!
I got recommended this video and the thumbnail gave me de ja vu, because I've seen it before. And I think it was four years ago as well.
I've noticed a lot of comments dated "2 weeks ago". Maybe this youtube channel is making a big comeback.
The youtube runs automatically sometimes as I sleep, I've noticed some weird dreams and feelings of deja vu with some videos...
This is really well done and appropriate for understanding the intuition of Bayesian probabilistic thinking. I teach this law to my Math students in grade 12 and I will show this video to them.
I whack it 1 - 3 times per day, I work from home
I realize I've been using this intuitively for years to fight my, or others' fears. But being able to quantify and codeify it is such work work of brilliance, I'm astounded. That's a smart person.
The trouble with updating beliefs while encountering new evidence today is we can all find evidence to support any belief. It really depends where one looks for said evidence. We all have so many information sources to tap now. So everyone can easily find whatever echo chamber they need, to reinforce whatever belief they hold dear.
Your statement is fully correct. It looks that statistics become more stable if you get more and more data. However the quality of data matters a lot too! And this is also included to the Bayes theory! The simplest example is having two Gaussian distributions, if you put them together, the tighter one will win, i.e. the more uncertain one has little impact. Indeed it is hard to quantify everything, but with the Bayes theory all is combined at least in a consistent way. If you want to get on something, the theory helps you not to loose.
Yes, you have to be honestly self aware to be able to use the principle - ie you have to ask the question "how would the data look in my personal echo chamber if I was wrong" vs "how would the data look in my personal echo chamber if I was right"? And you would honestly have to draw the conclusion that my echo chamber will still only resound the message I already have taken as true, wether my belief is true or not.
@@mattiasdavidsson7856so, Kamala or Trump?
You have to be able to weigh the quality of the evidence to the best of your ability and be honest with yourself of how good you are as a judge that evidence. Intelligent people tend to be realistic of their limitations while unintelligent people are overconfident - Dunning Kruger and all that.
Well said - this leads to a-priori vs a-posteriori and the implementations of mankind's laws compared to the laws that persist before mankind. The reduction of our illusions to the essence of what they are derived reveals more than most are willing to admit. That means change in the face of the ego's desire to remain inflexible. The forces that drive the game are that of care and desire and they are inescapably bound in this place. You will always desire something. You will always care to reveal the desire's outcome. To actually escape this issue is = _____ fill in the blank.
I've done a lot of repair work, and I know what's it's like to be in the category: "looks like he's going to rob you but really he's just doing his job." Let me tell you - every place is built differently, and you should always keep your eyes open.. One time I found a gas line going into a bedroom and not even capped off. The place would have filled up with explosives at the turn of a knob, well if not for my "snooping about" that is. But it's also part of the job description to not freak people out. I just said, "I need to look around a bit to make sure I know where all the gas lines are going."
That girl did not provide adequate background on stove repair. Like, old house, gas or electic stove. Why is this critical information? A good repair-man/woman, would look around to not only fix the point but also all connected to that point. Also, it would be so easy to inquire, why are you looking into bedroom/s? She phrases it snooping, which is secretly done, which did not seem to the situation/
Uh, I think that might have been because the video wasn't about stove repair. The details are rather incidental to what she was actually explaining.
She's in her thirties.
As a repairman also, I'll throw in my 2 cents worth. When you enter a house to do repairs you should always examine your surroundings to identify any potential exit points or hidden dangers such as friendly dogs that don't bite (been bitten twice).
Brew Sauce+ I've done a lot of electrical repair work, and it becomes second nature when entering an unfamiliar place to glance around looking for potential problems, to a point where one may not even be aware of it. And btw, I've spotted many problems -- shock and/or fire hazards -- that the homeowner was oblivious to. It is the responsibility of the electrician to spot these hazards, point them out, and recommend (even insist) appropriate remedies. I imagine it's the same for someone coming to repair your gas range (assuming it is a gas range). He would want to know if there any other gas appliances in the house, any lines/valves/couplings that might be problem, etc. It would be irresponsible to not ascertain this info.
Very cogently described. I am in awe of presenters like Julia who have such a great mix of intellect and articulation, great stuff!
Bayes' Rule is an important component of critical thinking. The ability to think critically is a skill that needs to be learned. The challenge is that common sense and intuition are often very wrong, and there's no trivial way for knowing when. It's on a case-by-case basis, and all those cases are about patterns that need to be recognized and examined.
Julia I'm guessing you're the math PhD because I would have just straight up asked Tom what his major is.
maeve main?
NOT BAD
damn maeve mains every where
lol
i didn't know people still played paladins lol
I have wondered what happened to Tom, he was my first friend on MySpace.
tchrisou812 oh Tom
Have you got him locked in your basement?
Tom is in the unemployment line.
He was my only friend on MySpace
Here I is
Repairman snooping around for the circuit breaker: Appliance repairmen sometimes have this weird preoccupation with turning off the electricity to an appliance before they work on it. 220 volts can really ruin your day.
In the UK at least, by law there has to be a circuit breaker within reach of the stove. In the US it will be split phase, so pretty hard to get the full 220v.
@@Tensquaremetreworkshop Most stove are run on 220V as well as electric dryers. Fools and high voltages can soon be connected.
Maybe he was looking for a bathroom.
@@walkergarya Yes, I know. And that is split phase, so 110 to ground. If you are not familiar with split phase, look it up.
It's not the VOLTAGE that kills you, it's the cardiac arrest.
These personal experience examples were amazing, helped understand it more intuitively. Thank you! Came here after crunching through some equations but these real world examples showcased the theorem in a very simple way.
Great, explanation. Your real world examples were very useful for me to think through. Thanks.
This is REALLY GREAT. I frequently come across content about how everyone is illogical that go on to provide examples of things i would NEVER do. These mistakes that you are teaching to guard against, however, are ones I know i do fall victim to and thus need to vigilantly guard against
And you do a good job providing practical ways to guard against them
If only i knew more people whose difficulties with logic, consistency and constantly affirming their pre-existing narrative weren't caused by far more basic deficiencies - usually deficiencies in CHARACTER at least as much as logic itself
I had a rudimentary understanding of Bayes theorem prior to this video, but now I feel like I really understand it. thank you
The fact that there's so many comments here along the lines of "wow, this totally changed my perspective on everything" is quite unsettling to be honest.
But positive.
Didn't find any, and that's unsettling too
well, It is reflected in the politicians most people choose.
ok why did a bunch of people get this video in their feed... pls comment.. what did u last watch?
@@sasisarath8675 "How to rob people by pretending to be a repairman"
The willingness or openness to challenge your initial impressions, and subsequently alter them, is a component of the attribute we used to call "humility". It has more to do with wanting to see things accurately, than it does with some false sense of being humble.
Your first example is right out of that book "Thinking, Fast and Slow " from Daniel Kahneman
Wow! This was very insightful. Even the way you calculated the conditional probability without using the formula and just using the areas instead.
_sees repairman checking out my bedroom_
_slams him against the wall_
"8% chance you're gonna rob the place, huh punk?"
"but sir, I'm here to repair your bed"
"Bayes would disagree .... get out before I call the police"
That would mean there's a 92 percent chance you're just an a-hole ; )
for some reason, the 'but sir' immediately made the repairman British in my internal narrative, making your story even more absurd, thank you sir!
Odds are he either likes your house, or is shocked to disbelief at the mess!
I just read:
sees repairman checking out my bedroom
slams him against the wall
1% chance this is an adult film
Why is "Bayes would disagree" both the toughest and nerdiest line at the same time.
Your videos have added that extra weight to my priors I need to convince me of the merit of Bayes Theorem. I'm committing myself to practice Bayes thinking. Thank you!
My friend; Bayes Theorem is running and operating regardless of your commitment status. To me, the video is a statement and not a proposal.
@@gyrojomo
Your perspective is of equal relevance to me, a 3rd party stranger. And perhaps OP's statement can nudge one more person into accepting the rationally sound choice of incorporating Bayes Theorem into their lives. That is a non-trivial post, but yours seems negatively intended and leaves me wondering, for what purpose?
@@gyrojomo dude. I don't want to assume you meant to be rude, so you should really work on how you relate to other people. That was painfully awkward to watch.
Very informative and probably useful as an introduction. Neat presentation, especially the graphics.
I never update my priors.
In fact I would have assumed the repairman was wondering where he was gonna lay me out after eating my liver with some fava beans and a nice chianti.
Fake repairman is the oldest cannibal trick in the book.
which is why you're still here to tell the tale ...she's trying to lead us astray ...thank you
I just phone for a pizza delivery -guy-
That's seems like adaptive bias, where we adapt to minimize the cost instead of the actual probability
i laughed out loud at this
I like a nice Chianti. Am I a cannibal? D:
Got a good chuckle out of the mathematician joke actually.
+Daniel Korolev that was good joke
Couldn't help smiling when I head the words 'Berkley' and 'snowflake' in the video. Hard to imagine extremely intelligent people becoming snowflakes. But may be there is no correlation between intelligence and wisdom.
Not saying the presenter is a snowflake. But I see a lot of young people take positions that would be considered 'progressive' in their eagerness to 'look' elite among their peers.
+B-Rad that's exactly what I am talking about - Classic elitism. I should have also added that this behavior has to do with conforming with 'views' spread by the progressives elites, so one could look like them. It is implied in my statement, but seems some people need more clarification.
Let me guess, you 'think' to care about animals & environment means to not eat them, because you have 'learned' this info from material that you read or watched on T.V or the internet. If you tell me you have a psychological problem to kill and eat another living, breathing thing, I will probably excuse you. But, the loving animals and earth etc is baloney. You just don't realize it is baloney - that's all.
If I prove to you that vegetables and plants also perceive pain..... my bad, this has already been proven. (Read about scientist Bose's work from more than a 100 years ago) Will you stop eating food altogether?
Those studies which claimed to prove that plants experience pain have been debunked. It's not true.
sez who sbunny ?
As to the final part, "Update incrementally", it is good to keep in mind when doing so that forming a general principle based on personal exposure, even if to many adherents, is still anecdotal not empirical, and thus influenced by the persons own biases or the context of the social norms. So in Berkley, where there is a lot of new-agey sentiment there are more people who feel that meditation is beneficial and this in and of itself can increase ones own personal perception of benefits, or if formulating opinions based on informal tallies of personal interactions, lead you to think, well it must actually have positive benefits because so many of those I encounter say it does. It is much like if you went to Brigham Young you would find many more people who said that prayer caused changes in the world or if you were at a Rainbow Gathering you would find a high percentage of people who felt LSD expanded your mental abilities and capacities.
Well said! That incremental exposure to an idea is how advertising works. One would be better off to let the positive words from a respected friend lead them to research the scientific evidence of the changes that, in this case, meditation makes in the brain as shown in brain imaging/scanning..
Excellent video. Really makes the theory understandable.
What a great way of illustrating this. Thank you!
Another important clue that Tom is a Math PhD student: He's walking. MBA students travel around campus in golf carts that they stole from the campus maintenance department.
Exactly.
Remember your priors!
remember your priors, how likely is it that a math PhD has the courage to venture outside of their room and into the savage social environment of the campus
It was the 'university campus' bit that got me. If you'd said 'federal prison' it would have been perfectly obvious.
Problem #1: When an accident happens, what is the probability that the accident is caused by a bad driver, given that:
1) 90% of the population has been involved in at least one accident
2) 30% of the population are bad drivers (means 70% are good drivers)
3) 99% of the bad drivers are involved in at least one accident
P(Bad Driver) = 0.3
p(Accident|Bad Driver) = probability of a bad driver causing an accident = 0.99
P(Accident) = 0.9
P(Bad Driver|Accident) = probability of an accident caused by a bad driver
= 0.99 * 0.3 / 0.9 = 0.33
= 33%
When an accident happens, there is only 33% chance that the accident is caused by a bad driver.
---------------------------------------------------------------------------------------------------------------------------------------------
Problem #2: Find the chance of having cancer, given that the customer is 65 years old.
Facts:
(a) 1% of the population have cancer (99% don't have cancer)
(b) 0.2% of the population is 65 years old
(c) Of those that have cancer, 0.5% of them are 65 years old
P(Cancer) = 0.01
P(65 yr old) = 0.002
P(65 yr old | Cancer) = 0.005
P(Cancer | 65 yr old) = What percent of the 65 year old population is likely to have cancer
= P (65 yr old | Cancer ) * P (Cancer) / P(65 yr old)
= 0.005 * 0.01 /0.002
= 0.025
Only 2.5% of the 65 year old population is likely to have cancer.
---------------------------------------------------------------------------------------------------------------------------------------------
Problem #3: Given the following:
(a) 1% of the population have breast cancer (99% don't)
(b) 80% of the mammograms detect breast cancer (20% don't)
(c) 9.6% of the mammograms detect breast cancer when it's not there (90.4% of the tests correctly return a negative result).
You have got a positive result.What are the chances that you have breast cancer?
P(Breast Cancer|Positive Result) is what we have to find.
P(Breast Cancer) = 0.01
P(Positive Result|Breast Cancer) = 0.8
P(Positive Result) = We need to consider both positive and false positive
= Positive + False Positive
= You have breast cancer and you have been correctly identified as having breast cancer + You don't have breast cancer but have been identified as having breast cancer
= 0.01 * 0.8 + 0.99 * 0.096
= 0.10304
P(Breast Cancer|Positive Result) = 0.8 * 0.01 / 0.10304
= 0.0776
So, if you have a positive result, there is only 7.76% that you have breast cancer.
Problem #4: Spam detection
(a) 50% of the emails are spam
(b) Out of 1000 spam emails, 110 contain the word 'Nigeria'
(c) Out of 1000 non spam emails, 48 contain the word 'Nigeria'
A message with the word 'Nigeria' arrives in your inbox. What are the chances that this message is spam?
P(Spam|Nigeria) is what we have to find.
P(Spam) = 0.5
P(Nigeria|Spam) = 0.11
P(Nigeria) = Probability of a message having the word 'Nigeria'
= Probability of word 'Nigeria' appearing in a spam email + Probability of 'Nigeria' appearing in an non spam email
= 0.11 * 0.5 + 0.048 * 0.5 = 0.079
P(Spam|Nigeria) = P(Nigeria|Spam) * P(Spam) / P(Nigeria)
= 0.11 * 0.5 / 0.079
= 0.69620
There is a 69.2% chance that the message containing 'Nigeria' is a spam.
Clever. There is a 99% chance you are a mathematician but since I am not, my view of probability and judgement is skewed.
xazzbi Yes, just draw the rectangles as in the video. Instead of Math/Business you have cancer/no cancer, and instead of shy you have "positive result".
P(Cancer) * P(65 yr old | Cancer ) represents the Probability that someone you know nothing about has cancer AND is 65 years old (first you take P(Cancer) since you know nothing about that person and then you multiply P(65 | cancer) since the cancer part is already included in the first probability).
Now you have the "pool" of people who are both. But since you know (in the problem) that the relevant portion is 65 years old you have to divide by that probability to include that knowledge.
Proof (I know it's not helping to visualize :P):
P(Cancer) * P(65 | Cancer) = P(65&Cancer) = P(65) * P(Cancer | 65)
P(Cancer | 65) = P(65&Cancer)/P(65) = P(Cancer) * P(65 | Cancer) / P(65)
It should be noted that the conclusion of problem #3 only applies if you randomly test people from the population. If you were prescribed a mammogram to begin with, there are other reasons why your physician suspects you might have cancer, and therefore belong to a population that, even before testing, has a chance of having cancer higher than 1%. Also, is your figure of 9.6% of false positives a real one or did you make it up?
Good way to refine probability judgment. Thank you!
I couldn't help being distracted by that light switch just left of your head, so . . .
Bayesian thinking:
1. By your accent, you are probably American filming this in the USA.
2. Common US building code makes the top of the light switch about 4' high.
3. By making a quick judgement call, if you were standing up for this video your height would be about four foot, three inches.
4. By my experience the percent of adult women in the US who are only that tall is less than 1%.
5. I am adjusting my perception of you standing in front of a wall to perceiving you seated in a normal chair talking to a camera on a tripod.
Okay, I am subscribing to your channel.
Maybe the light switch is just low down.
That is just in your head Scott. She just wants to explain things right in the video. And she does. There isn’t any more to this video.
Spot on. Very insightful.
Hey Scott: what percentage of women's garments are low cut? Have a look around the stores, I'll wait.
@sk54931 Perfect height for a woman that is, yes.
This reminds me of a Government ad I used to hear on the need to wear seatbelts. It basically said you need to wear your seatbelt even on short trips close to home because something over 50% of all accidents happen within 5 miles of home. And, well, duh. 99% of all miles traveled in cars is within 5 miles of home. Anyway, 87.32% of all statistics are made up on the spot.
puff puff give willie
I think it makes sense though, if people are not wearing their seat belt because they think that since it's just a short trip they don't need to. So, it is countering an inappropriate instinct. Because maybe people don't think about the cumulative distance they are travelling in short trips.
yeah on the spot, just like you made up 87.32
@@rohithipparkar707 That's the joke.
Steven Wright once quipped “Someone told me half of all car accidents happen within a mile of your house. So I moved.”
I just love how Julia express her ideas, very clearly.
In 2002, Angela Cannings of Salisbury in the UK was convicted of murder in the death of her second and third children, apparent victims of Sudden Infant Death Syndrome (SIDS). The prosecution argued that the probability of a single instance of SIDS is 0.004% and therefore probability of a second instance is so small that homicide is the only likely explanation. The conviction was overturned on appeal when a statistician testified that, while the probability of two SIDS deaths in one family was vanishingly small, the probability of two infanticides by a healthy middle-class mother was actually much smaller. This is what can happen when you don't remember your priors!
Jim McDonald that’s not what happened at all. The problem was with the assumption that sudden infant death syndrome events in a family are independent events. The expert witness in the first trial believed this. But on appeal they found a different expert witness that showed they are not independent events and that sudden infant death syndrome has been shown to be influenced by inherited genes. It wasn’t overturned because the probability was indeed vanishingly small but double infanticide less so, it’s the fact that it isn’t vanishingly small at all!
A better example is the early use of DNA evidence. Probabilities of marker matches were given as if the suspect were randomly chosen from the entire population the DNA database was based on (naive frequentist). Of course, the actual pool of plausible suspects was normally limited to people in a single community or sometimes even a single family, where the probability of sharing particular markers can be quite different. Gets even worse when talking about multiple markers and their joint probabilities. There are details I'm leaving out, but that is the very general idea.
This was all put in frequency language, but it blindingly obvious if you just use a Bayesian framing.
My PhD adviser (population genetics) actually testified in court as an expert witness against DNA evidence in some of those early cases; then turned around and testified in support of DNA evidence (including some Innocence Project stuff) once the FBI got their shit together on the statistics.
All this proves is that our society is incredibly gynocentric and women are allowed to get away with murder. The UK is known for being REALLY bad about this. I wonder what they did if she killed a 3rd later on: www.telegraph.co.uk/news/2017/05/16/oxford-student-spared-jail-extraordinary-talent/
Also, no statistician "proved" that the probability of 2 infanticides by a middle class mother is much smaller. If she kills once, she's FAR more likely to kill again than a RANDOM OTHER female member of the population. I don't believe for a MOMENT that this was legitimate math. This is gynocentrism. The pussy pass.
I would also imagine that multiple incidences of SIDS occuring in proximity wouldn't be a true statistical anomaly since the deaths could have been caused by the same factors.
I didn’t know this had a name. I thought it was simply being curious and not judging a book by its cover. I’m glad it resonates with people and I hope they’ll adopt it and apply it to everything happening these days. Because these days people think they’ve read the book because somebody on social media recommended it to them.
I've always liked to use something close to this general thought to keep my analysis, general guesses and knowledge of stuff updated and changing, avoiding fixed preconceptions or prejudices. This is quite similar in many ways to my personal system, although I haven't put it down in numbers or created clear rules and patterns, it was more psychological and simple.
It's very interesting to find something close, and makes me even more interested in the possibility of studying statistics, something I already like a lot, but don't know if I like enough to live on it.
Thanks for this, I think I first saw you with Matt Parker on Bayes. Keep up the great job. Every detail can have a small influence on coming to momentary (?) conclusions, always doubt yourself.
I can't believe I took so long to find this channel.
I don't know much about meditation, but as far as I do know, meditation is nothing more than you practicing to control your racing thoughts. And as we all may know, the more you practice something, the better you get at it.
@Fernando Cunha I'd actually say that it is incredibly simple once you get the hang of it. What could be simpler than winding down? I've done it for 10 years and I love it.
I'd also just say that it is more about being attentive and open to yourself than about actually wanting to controlling your thoughts, though it's true they will become calmer and more focused.
I would agree however, that without some practice in a meditation centre under a proper teacher it can be difficult to get the hang of it by yourself.
I highly recommend the books and talks (a lot of them are in youtube) by Thich Nhat Hanh (vietnamese zen master). He speaks plainly and powerfully, in a way akin to science. He likens zen theory to Lavoisier's principle of the conservation of mass. And you can feel that he is largely free from attachment and dogma.
I just understand Bayesian statistic after 1 year of confusing because of your video. Thank you!
This is great, particularly the animation of updating your priors after receiving new information like in the meditation example. Most people only update their priors when they get a result that confirms their previous bias.
I reluctantly agree. And I perceive that social media, with its stovepiping algorithms, exacerbates this. One can, almost without noticing, end up in silos where there is a high degree of conformity of opinion, and where differing views are subtly, or not so subtly, marginalized.
In my own case...though I try to avoid confirmation bias, I have no doubt that I'm afflicted with it. It's easy, maybe even comforting, to be surrounded by people who agree with you, and to latch on to tidbits of info that confirm one's vested position. OTOH, when I re-think a position, based on new evidence, or even a compelling personal testimony or someone eloquently putting forth a different view, it feels liberating.
But remember, she has the scout mindset (and not the soldier mindset) !
This seems like a good way to justify your position while also being wrong. I like it.
Late to the party, but best comment. This is Bayesian Feelings. Even got the formula wrong.
maybe he was just nosey, it sounds like an episode of law and order
Maybe he's in the middle of designing a new house/decorating ... bottom line, assume nothing. At the same time though, trust no one ... ...
I had the same thought when she mentioned meditation. How can sitting down and doing nothing be 'fake'? More like 'I dont have what it takes to do it, so I'm gonna call it fake to convince myself it doesn't work'
Why would you like something that encourages falsity and error? Are your feelings more important than discerning the truth (which is the basis for this whole video)?
I've been struggling to "get" bayesian stats for a couple of years, sorry to say, because even in my technical work (biomedical informatics) I need visual representations of abstract relationships to help me think through problems. So your visual aids were extremely helpful to me. They took a rather wobbly abstract concept of priors and offloaded them to a visual concrete representation to reduce cognitive load. Thanks so much and I've subscribed to see what else I can learn!
To me, it's a cognitive load even after visual representations. One is either numerically/scientifically predisposed or isn't. I don't think you can force yourself to become adept at something you're not naturally adept at.
Thank you for this video. I really like how you show that mathematical thinking can improve your life. I do have one quibble and that is that it doesn't seem like you are applying Bayes' Rule, it seems like you are applying conditional probability. As I understand it, Bayes' rule shows the relationship between P(A|B) and P(B|A). If I knew the probability of someone being shy if they were a math student, and wanted to know the probability of them being a math student if I had prior knowledge they were shy, that would be an application of Bayes' rule. Conditional probability is a concept that predates Bayes' rule. I may be missing something which you can explain, but in any case thank you for the fine video.
based on this video i am going to predict you will make more videos with light switches in background
hilarious, was laughing for 2min :DDD
Right on. I can only remember this talk as the Light Switch Theorem
Your 'prior' that the switches are majorly for lights needs to be updated.
I was reading an old newspaper and came across this theorem, thank you for clarifying!
why were you reading an old newspaper?
I got an odd sense of deja vu while reading your comment.🤔
do you even know what a theorem is?
Old newspaper? As in, UA-cam would only play at 480p in it?
Ever in your life did you wish you had a Hurdy Gurdy?
Man I can't wait for this to be implemented in the next patch.
Think more as wise as how I stopped here
Vs
Think more as wise as how I understandably win a particular argument with you
This is a really good explanation. The weakness of Bayes is hidden in Julia’s explanation, though. Namely, so often the probabilities aren’t really probabilities but just numbers that people make up. This can lead to a sort of confirmation bias. A fairly easy example of this is the question of whether humans are the only life forms in the universe. There is currently only one example of life, so we really don’t know how likely life is given some set of priors. People who think there is something special about Earth will give a completely different number to someone who doesn’t. Consequently, two people using Bayes to ask the same question get totally different results and coincidentally (not) they get the answer that supports their preexisting belief.
This isn’t meant to say that Bayes is useless. It’s not. We just need to be aware of where we are using real numbers (students in a PhD program) versus made up numbers (how likely someone would diagnose a business major of being shy).
Bayesian stuff is all about updating the 'posterior probability'. As new info is gained one adjusts the priors and get more accurate probability determination.
So one could start with total unknown prior of 50% and still get useful Bayesian results. Note: my current understanding of this. Actual Bayesian application in real situations is very complex. A good book is 'The Book of Why; The new science of cause and effect.' by Judea Pearl
Corresct: We just need to be aware of where we are using real numbers (students in a PhD program) versus made up numbers (tentatives to fix the probability os inteligence life)
I think people should learn Bayesian from its statistical development. Bayesian method in psychology is just scratch the surface.
Sources?
Damn. You're a good teacher, I actually learned something.
What an amazing video this was!!! I just subscribed!!! Wonderful!! Hats off man!! You definitely deserve much much more subscribers mam!!!
Bayesian thinking is a tool that may help defuse prejudices.
This is one of those rare things which feels like a bug fix to the brain
machiavellian thinking is far superior to this crap
Rare? Mate, all I fucking do is troubleshoot this buggy piece of shit.
@@creamwobbly tomayto tomato
@@LowerYourExpectationsPleb what are you on about, those two don’t even have to exclude each other
This is such an amazing explanation. Thank you so much!
Hi, Julia. I just stumbled on your channel. Thanks for this! And an observation: I'm struck by how similar Bayes's style of thinking is to David Hume's. I imagine there's some already well known connection here.
Meditation is real, the mind is a real rabbithole. I accidently stumbled upon a type of walking meditation. It shifted my mood and how I prioritize things for a few weeks. I was very productive, the effect was acute and obviously to me had began after the meditation experience. But I was unable to reproduce it.
i believe you! ....that is because you can only move forward to the next level of meditation and can never remanufacture a previous season of it as it is a spontaneous newfound prayer which is nestled between two eternities which shall never occur again! we go from faith to faith and from glory to glory! Eventually, if one continues in meditation to its supernatural end, you graduate from meditation into contemplation, which is effortless perpetual spiritual prayer without the use of the natural carnal intellect!
@@clarkkent3730 It seems to me more of a natural thing, but to each their own.
a math professor i sort of knew meditates often
Critical and analytical thinking... a virtue possesed by only a very few. It was refreshing to watch. Good to know like minded people exist.
I've never thought that my constant complaining about people implied to them that I was jealous lmao
For sure a reasonable percentage of people who know you have come to that conclusion.
i joke about this a lot but that doesnt mean i believe people are actually jealous of me
Think more to not be fool either by how others testedly testing my way of knowledge perceiving life...
Vs
Think more just like I know what my hands did in an hour, a day, a week, a month, a year and how I bestowed on the outcome of it regularly
I used to dismiss the word "intuition" the way you used to dismiss "meditation". The way I heard it often used was like a person were saying, "I'm making this claim without any evidence at all, based on my emotions, and any challenge will be deemed hostile". The implication is only a little exaggerated there, but you've likely heard "intuition" used as frivolously.
Eventually, though, I heard someone discuss a subconscious thought process -- the idea that the brain is recognizing patterns seen before. Example: Mom tells teenage daughter the new boyfriend is no good for the daughter. The subconscious part is that the mother has seen males with similar behaviors and speech, and those males were no good, the "love 'em and leave 'em" type, for example. While Mom may not know what details mattered, the subconscious triggered anyway.
So while some folks still might toss around "intuition" carelessly, for others, there is probably something to it.
Agreed on the theory you described of how "intuition" is built. It's a sub-conscious pattern recognition process. The big problem with intuition is, that it is anecdotal and completely depends on your own life experience. In your example: What if mom, had only met an outlier group of males for which the behavior seen indicated they are bad as a partner (but hasn't been exposed to the normal population of males that exhibit the behavior but are good partners?) This is obviously possible, but the intuition mom built, based on her sample would be completely wrong... Intuition is not bad per se, it's essentially a short cut that can save us from analysis paralysis, but it can go off the rails very quickly...
Probably(well, decently often anyway) they know something/or can see a pattern you don't. Thus you think their claim is arbitrary.
Intuition is really just picking up small details unconsciously, you put them together later and come to a conclusion. I'm no mathematician, but a lot of what she's saying is part of normal thinking, and no doubt contributes to what we call intuition.
Just like the words 'narcissism and narcissistic', they're being used carelessly by those who don't know what it really means.
I think you've reduced and presented a complex issue very well. A sub from me!
love your channel
What kind of watch is Thom wearing? Is he wearing a vintage Casio calculator watch from 1985?
Kinda cool - thank you! "What if I were wrong. What would that look like?" Damned good thing to ponder. Great basis for critical thought.
basically, consider everything before casting judgement. I agree.. also accept that you could be wrong. also I agree...
more like consider likelihood of event happening due to volume/sample size.
If sick person vomits 5/10.
If healthy person vomits 0.5/10.
There are 4 million healthy people.
There are 1000 unhealthy people.
So, 200000 healthy people are vomiting.
500 unhealthy people are vomiting.
A person vomits. He has 1:400 chance he is sick, vs 400:1 he is healthy. 400 x more chance.
@@troooooper100 I love math. but that's too much math every day... but thanks 😅
If you found the math joke funny, what is the probability you are a mathematician?
Depends. Are you shy?
Probably pretty low since the probability of being a mathematician, in general, is fairly low
I think he/she meant the probability of being a mathematician without practicing mathematics or studying it.
If you didn't find the math joke funny, what is the probability you are a mathematician?
Awesome self-reference loop into the prior prob topic!
The issue with this that I can find is that, in these examples, you're still pulling percentages and ratios out of thin air. Now granted, you're trying to correct an assumption on the fly. But correcting an assumption based on more assumptions, you can still be wrong with your initial set of assumption. For instance, maybe repair men aren't more honest than not. Maybe thieves are very common among st repair men in your particular neighborhood?
...and a new religion was born
Those would be included in the prior. P(he is a thief | he looked like he was snooping) = P(he looks like he is snooping | he is a thief) * P(he is a thief) / P(he looks like he is snooping).
Your priors have your estimate of P(he looks like he is snooping), P(he is a thief), and P(he looks like he is snooping | he is a thief), however it is that you came up with these quantities. All the things you described are just things that could be taken into account when your priors are determined
Abscence of evidence is not evidence of abscence. Turkey problem. you are right, wrong assumption, no negative scenario considered.
couldn't it be partially remedied with exaggeration and underestimate aka considering the best/worse case scenario? that's a super high percentage for shy math students (75%) and super low percentage for shy business students (15%)
I look at new information on whether it's persuasive. I used to work in legal research. If I was right with the proper rule and information my idea was unshakable and irrefutable. Other times I had to concede I was wrong and I knew exactly why I was wrong. I always learned something new.
Minor point, but... when it comes to mental health, a consistent placebo effect is better known as a "cure". If something makes someone happier regularly, calling it a placebo effect is kind of meaningless, no?
maybe in the realm of mental health, it could mean that it might seem to be working to cure their mental issues, but is actually only demonstrating short term cures and nothing permanent or in the long term. Depends on what the context and goal is though, I guess.
That math joke was pretty funny lmfao
I like her thinking.
Reminds me of little Johnny in class. The female teacher hides a fruit she gets out of a bag behind her back and says, “Class, I am holding a fruit behind my back. It’s long and it’s yellow. Who can guess what it is”?
Little Susie holds up her hand, then the teacher calls upon her, and she says, “it’s a squash”.
The teacher displays the hidden fruit and says, “No Susie, it’s a banana. But I like the way you’re thinking”.
The teacher then secrets another fruit from her bag, hides it behind her back, and says to the class, “I am holding a fruit behind my back. It’s round and it’s red. Who can guess what it is”?
Little Mikey holds up his hand. The teacher calls upon him and he says, “It’s a cherry”.
The teacher then displays the hidden fruit and says, “No Mikey it’s an apple. But I like the way you’re thinking”.
Little Johnny then asks if he can hide something. The teacher thinks for a second and says yes.
So Little Johnny puts one hand in his pocket and says, “ Teacher, I’m holding something in my hand. It’s round and it’s hard. Can you guess what it is”?
The teacher blushes bright red, then becomes enraged, and says “Little Johnny, we will not have any such vulgarity in my class. Go to the principal’s office right now.”
Little Johnny then displays what he was holding to the class and says, “Teacher, it’s a quarter. But I like the way you’re thinking.”
Great vid. Wish I had discovered you 9 years ago when you did this! Subbed!
The virgin math PhD vs. the Chad Business major.
If I had a PhD in maths I wouldn't care about being a virgin tbh. That wins every dick measuring contest anyways.
@@MrCmon113 The virgins are evolving.
Actually math PhD makes hella more money than business major
lol i was afraid to find comment
@@rephaelreyes8552 Yeah that's why mathematicians have all the private jets, super cars, and hundred foot yachts, and they get aaaaalllllllll the bitches.
LOL shut the fuck up.
There is scientific studies about how meditation works. But there is a basic logic on meditation, a person who takes some time every day to just stop everything and stay calm with the eyes semi-closed and try to keep his mind calm and open for a period of time... if he/she do it periodically then of course his brain and nervous system will work in a different way than a person who never trains to be calm and is always overload with emotions. I do not understand why somebody would think that "meditation is Fake". The mere sentence doesn't even make sense, you could think that meditation doesn't produce results, but the act of meditation itself is not fake, even if it didn't work, you did it and "wasted your time". Also this means that meditation is poorly understood by people who don't know about it, often they think it has something to do with superstitious phenomena, when instead, meditation is just what the word implies: thinking deeply. There is different types of meditations: for instance watching your video is a meditation, specifically an Analytic Meditation. There is also abstract meditations, but I'm sure you get the point, if you spend some time with no physical activity whatsoever, no external supporting tools, only using mental tools to make your mind work in either an abstract or analytic way, then your mind will evolve, and even physically your brain will adapt to that kind of training and improve (if your meditation is aimed in the right direction, of course) because as you may know, the brain's cells ability to re-order and create new synapses is quite remarkable, so this should give us a clue to why meditation works. Look at how the odds are low for meditation not "being real" that even if it was a "placebo" you missed the point that a placebo is a result of the mind thinking something is helping so the results shows it is working... THE MIND, a placebo is one of the features of the mind influencing the whole nervous system and the body (and that is a tool of meditation). As you may see, that square is still not drawn in the right way, even after you corrected it... I am sorry your video is great, you are amazing... I think that's why it really destroyed me that initially you thought "meditation is fake".
Calling it fake may be a lazy/overly-broad way of saying that mediation is so poorly defined, on top of being a subjective self-reporting, that it's tough (impossible) to find any reason to believe it can be definitively found to be efficacious. Consider cognitive behavioral therapy (CBT) and its successful track record. Is CBT a set or subset of meditation or vice-versa. Do they need to be teased apart? CBT involves exceptional concentration via structured introspection. That act overlaps with things that take place while engaging in various forms of meditation. But it doesn't require focusing on breath, or finding your center or any other aspects. So telling someone that a bit of structured concentration can do wonders for you is as valid as saying meditation works. It shouldn't come as a surprise that active management of your mental dialogue (including 'clearing your mind') can yield positive results.
Well said, Eagle Dee. They might be more "in control" of their emotions and less likely to be bouncing between addictions or merely reacting to stuff. Maybe they over eat less.
Why did I end up here? At one moment I was on Sadhguru's video, then FFVII guitar medley, then suddenly....
that is youtube for you
haha - perhaps youtube knows statistically that some of the people who study Sadhguru are interested in both inner and outer Sciences .
the same here i was watching for mic sound qualities, maybe maths and sounds goes together who knows....
I was watching a Mariachi Guitar Lesson...WTF ?
My thoughts exactly Leon!?!?!
Super useful and accessible content, nine-years-ago-Julia!
How do you assign probabilities to something like "meditation works?" There is no definition of what constitutes achieving a meditative state, and no precise goal of self-improvement that might be fostered by the practice. Coherent terms matter. Also, the assumption that one's "priors" were, themselves, correct is questionable. I'm not saying the Bayesian principle isn't useful; you just have to remember its limitations.
With that example, in particular, the priors got "updated" based on new information. The priors are seemingly arbitrary but it is important to keep in mind that they can (and should) change based on new evidence. It's important to be aware of priors when making assumptions about observed events, as it is far too easy to make a number of logical fallacies otherwise.
You do indeed have to be aware of priors when making assumptions; I think the point I was trying to make is that assumptions underlie one's assessment of priors.
First you should obviously define for yourself what do you mean by "meditation works", what is it supposed to do if it is "working". In this case it seems that meditation is supposed to make you feel happier, and the question becomes, "does meditation make you feel happier?". And that can very much be evaluated, just ask people who started meditating if they feel happier after they started, that gives you at least some weak evidence.
Now personally i think its quite sufficient to believe yourself to be happy in order to feel happy, healthy brain chemistry should take care of the rest.
Given that only people who start out with belief "meditation makes you feel happier" are likely to actually try doing it, it becomes obvious how meditating can create belief that you are supposed to be happy followed by actually feeling happy.
So on the surface, it would seem "meditation works", but no theory is much good if you don't try to falsify it, so how would you go about it. In case of my pet theory, one could gather a group of people who don't believe "meditation makes you feel happier" and convince them to try it anyway(for the sake of science/pay them to do it) and gauge their perceived happiness levels before and after. One can imagine the end result.
Then perhaps you can add a caveat to "meditation makes you feel happier", "but only if you expect it to" and thus gain new understanding of how happiness actually works.
What Jan said. Both times. It very, very, very often trumps everything, regardless of how soundly the mathematics were applied.
That is how for example the United States Congress passed a bill to increase the amount of Medical Care (and as a bonus, add administrative cost!), and actuarially state with a straight face the it would REDUCE overall costs!! This actually happened in the U.S. in 2009. "It's the assumptions, stupid!"
That’s why ya gotta operationalize your terms
I didn't like the meditation and the jealous guy examples, because in those scenarios the probabilities are completely made up, and you only get a confirmation bias of what you already expected to be very probable. Bayesian can be very tricky...
You missed the entire point bud. Zoom out a bit. Those subjective examples are perfect _because_ they are not precisely defined and are ill-suited for "real" scientific study. The point of these examples is to illuminate Bayesian _thinking,_ which is different from _applying_ the Bayes' model to determine whether Bob is jealous or if meditation makes people happy. A real example with objective results would detract from this video's purpose because it would be easier to miss the point by getting caught up in, "Oh cool, meditation works," or, "Dang, so Bob WAS jealous. I knew it." With the examples in this video we instead see the process by which we might organize different factors and note changes in them; hell, even just noticing that there will be changes is stressed -- e.g. "update incrementally." The point of this video then was not _to_ conclude answers to _these _*_particular_* questions or problems, or even to demonstrate that these questions or problems can be answered or solved; the point of this video was _how_ to conclude answers _across a broad range of _*_possible_* questions or problems.
i hope she replies, dude
TurdFurgeson571 You did not consider another possibility, which is that her examples actually demonstrate why statistical reasoning is often misleading. To put it succinctly, probabilities do not prove causalities. On top of it, most mathematicians I know do not consider statistics to be a branch of mathematics. It is not difficult to find out why.
@@pawelpap9 I doubt that a video titled "... Bayesian thinking" is going to delve into the pitfalls. This seemed to me to be a broad overview. For her to go from this 30,000 foot view down to the more granular discussion of how stats must ultimately be interpreted, which opens us up to reading the data in a misleading way, seems like too big a leap for even the most novice content creators or script writers, so it just doesn't seem like the purpose of this video. Additionally, if that is her intention, she's being awfully coy about it, rather than just coming out and saying, "Be careful."
The jealous guy example worked well, because the point was she had a lot of evidence prior to believe he was jealous, therefore the area of the jealousy square was larger. I think you just misunderstood the point.
Good logic. I've cultivated this in myself, though I never knew a particular name for it.
Now that we coming up on the 10 year mark, we need a visual guide to Bayesian sinking.
This is the kind of woman the media should be giving exposure to, and not the Kardashians of the world, if we start valuing the pursuit of knowledge, with acknowledgment, money, fame, etc the society will be a better place for all of us.
request for update: I would be interested in seeing this process applied to pro/anti-vaxx thinking, particularly w/respect to the covid pandemic
Was getting my first shot yesterday and feeling a little anxious and then looked around at all of the people around me and imagine the room being full of this many people constantly, every day for weeks and I hadn’t heard a single issue on the news in my city about any problems so that made me feel better. Funny thing, it doesn’t work for me on plane rides, though. I think about how there’s 5k+ flights every day in US and no accidents so what are the odds THIS one will be the one. Still doesn’t work for me. Still sure I’m going to die every time.
Are the light switches significant?
Yes, they show she is likely seated. This leads to some interesting "priors" possibilities....
Where have you been for the last year, Julia? I love your brilliant videos.
If you were my teacher I'd actually be early for something.
Scott Rensel you're a lost cause anyway
@@Emile.gorgonZola You're a moron. Go fuck yourself. :)
@@Mithranos Come on, that was a pretty funny jab. The person knows nothing about you. It's obviously a joke and not personal.
This is why I love teaching math...because most kids see numbers ...get confused...and leave me alone.
So this in stats:
1. Be aware of Availability Heuristic.
2. & 3. Be aware of confirmation bias.
Aka, logic in philosophy. Well a component at least.
Thank you for this video. Your examples are super enlightening and I feel like you've communicated the idea of prior and posterior probability better than my own theory of probability/statistics classes.
One thing I wanted to mention, though, is that I think we need to change the way we think about the term "placebo" (and I'm very guilty of this myself). You say that the placebo effect could be evidence that meditation is fake, but I'd argue that the placebo effect can also be evidence that meditation does work. If Bob expects meditation to work, and it results in him being happier, then the mechanism "behind" meditation ultimately doesn't matter because it works for him regardless.
The same can be said for placebos in double blind medical trials. If a person sees benefit from taking a placebo, unaware that it's a placebo, that doesn't negate the fact that they saw benefit from it. Sure, the placebo isn't "doing" anything, and there are definitely other factors at play that could be helping, but our brains are also weird and easy to fool. Anxiety is strongly linked with gastrointestinal health, and psychosomatic symptoms are still symptoms.
Just some food for thought!
If I see Tom I can see what Tom is wearing. That will ultimately narrow down one's guess. Given one or two more data points and you're well upon your way to knowing the specific kind of maths or business.
Judging a book by it's cover has kept a lot of people out of early graves.
@@WeighedWilson And has kept many a good book out of people's hands.
@@WeighedWilson Judging a book by its cover has also sent many to an early grave and caused misdiagnosis. Devil's in the details.
@@WeighedWilson Welcome to maths.
I feel like you could start with definition first and explain the definition. I felt lost in the long string of examples.
Does it seems wrong to anybody that 1:100 is 1%? I thought it should be 1:99...
Yep!
But 1 out of 99 isn't the same as 1 out of 100.
Think more the hardest way as wise as how I'm honest to myself, with every details of how I spend my precious seconds of every minutes of every hours....
Vs
Think more the hardest way even when I was supposed to be happy in a framely set-up man-made time-line schedule