I love this subject! I'm studying Bayesian methods in my PhD, here's my perspective: Frequentist reasoning wants to deal objectively with data, so it considers probability to be a property of the world; it says "the coin has probability 1/2 of being heads because that's the frequency of heads in the behavior of this coin"... and there's a right probability, it's a fact from the world, it can be learned by data that shows that frequency in behavior. Data is noisy, but it reveals true propensities through frequencies. Bayesian reasoning wants to deal logically with data, so it considers probability to be a property of logical propositions about the world; it says "the statement 'coin landed heads' has a certain probability of being true, it is 1/2 for me and 0 or 1 for you depending on what you see"... the proposition is connected to a point of view, and different points of view will differ in how close they are to the truth about the state of the coin. So probability is subjective in a sense, but all points of view with equal information should objectively agree about probabilities of their statements (it's objectively subjective, just recognizing the existence of different points of view, but they are not supposed to be personal, not opinions). When you update your "belief" over data, it's because data moved your point of view in relation to the "truth". In this example, once we see the coin, we update the statement "coin landed heads" from 1/2 to 0 or 1 depending on what we see (probabilities of 0 and 1 mean perfect information while 1/2 means no information). There isn't an actual divide between the two, theoretically... Bayesian reasoning recognizes the relation between frequency and plausibility, while frequentist reasoning recognizes points of view, it just doesn't go there.
So in other words the frequentists approach will give you a correct answer every time but may need indefinitely to evaluate, while the bayesian approach gives you a result immediately but this result may be wrong.
@@ndrsvgl hm... the approaches are answering different questions, both correctly... what is this answer/result that you say they are trying to give? in the experiment of the coin, we can arrange for the mutual agreement of the two approaches in every observable event (observable in the sense that it doesn't talk about probabilities)... for example, if you flip the coin and ask for the exact result it will give, both should agree in saying: "I can't tell"... if you say you flipped the coin a zillion times and aks for the proportion of heads, both should say immediately: "it's 1/2" (but they would interpret your question differently)... I guess you are talking about this difference: you ask what is the probability of you having a coin in your pocket. One bayesian could say: "I know nothing, so for me it is 1/2"... another bayesian could say: "I saw you handling coins before, and if I have a model for how probable it is for "coin handlers" to have coins in their pockets, I can update that probability of 1/2"... another bayesian could say: "I know that people in this city carry coins in their pockets with a chance of 30%, so it's 30%"... someone could say: "it is 80%, because I saw in the stars", but that wouldn't be bayesian, it's a personal kind of subjectivity... a frequentist would say: "i can't know, because I don't know anything related to the frequencies with which you carry coins in your pocket, i don't talk about probabilities for single events" now, those bayesians can't be right at the same time, yes? and that frequentist will take a long time to discover the frequency by making the situation become a repeatable experiment... the thing is, all bayesians are right, but their answers have limited power where the frequentist has no answers at all... it may seem silly, but that "imprecise" reasoning of bayesians has major applications, here's a very understandable example: en.wikipedia.org/wiki/Bayesian_search_theory
Bayesian and Frequentist are two thinking methods to answer different questions: what I know and what I should know. None are wrong, and it doesn't have to do with psychology or personality. It depends on the situation and which question should be answered first.
My interpretation is that the bayesian reasoning is correct, but the frequentist reasoning is easier for a variety of reasons so scientists often use it instead. I take this comment as empirical evidence for my claim, as the frequentist explanation takes about 1/3 of the words to explain than the bayesian.
As a psychiatrist, I feel like I rely on both Bayesian and Frequentist philosophies in my everyday work. When advising on diagnoses, I use the Bayesian approach. That is, I gather whatever data I can to inform an opinion (about a diagnosis), and then I update my opinion if and when more data emerges. I'm not overly invested in getting a 'right' diagnosis because a patient's presentation is dynamic and complex such that they can't always be reduced to a single category at all times. I'm happy to revise the diagnosis when necessary. But when I'm advising on risks (i.e. the risk of somebody committing suicide, homicide, arson, etc.), I use the Frequentist approach. I am infinitely more concerned about what will happen when a patient has had numerous repeated attempts at harming themselves or others because that informs the probability of how likely a person is going to repeat history. I think to myself, "what will happen if the patient attempts the same move another 100 times?" To me (and I'm not a statistician, although I know a little about human psychology), the Bayesian and Frequentist approaches are fundamentally concerned with certainty vs uncertainty. The Bayesian aligns herself with changeable opinions informed by available data, thus she is never completely 'certain' about anything since her opinions change when new data emerges. The Frequentist on the hand aligns himself with unchangeable facts based on logic, thus he is always completely 'certain' about everything as long as his logic holds water. The coin toss was a great teaching example. It was a great example because the answer was inconsequential. I mean... Who cares how the coin lands? Nobody was harmed in the making of the video, yes? (I hope). We can allow ourselves to assign equal weight to both philosophies in this teaching scenario when the outcome of the coin toss was inconsequential. I suspect people are likely to gravitate towards a Frequentist approach when contemplating decisions that are very consequential because the Frequentist approach feels more tangible to me while the Bayesian approach feels more abstract. So I don't think it is a matter of 'are you a Bayesian at heart or are you a Frequentist?' Rather, it may depend on the weight of the decision you are about to make. Having said that, I do acknowledge that some people are more tolerant of uncertainty than others, thus for those people, they are more likely to be Bayesian perhaps. Does this make sense?
It's less about the weight of the decision but the fundamental structure of the question. If you ask, "What is the probability I WILL flip a coin heads?" versus "What is the probability this is heads?" then this is the difference between the two thoughts and it doesn't matter the importance or the pertinence or the weight. So you are right in saying it has nothing to do with personality or thought process its just whether or not people are aware about the two different "modes" if you will of an outcome.
Do not mix human senses with the math. Both Bayesian and Frequentist approaches are mathematically solid and they converge when infinite data is available. F. put the uncertainty into sampling, i.e. we do not know the exact value because we only observe a limited subset of the universe and we can make an estimate of the interval where the true value can be. B. put the uncertainty in the value itself: as we have limited data available (including prior knowledge) we can say that the value in question can be drawn from a distribution. So instead of a point estimate B. give you a distribution of values. There is no more correct or less correct approach, it depends on what you want.
I like this approach! It definitely depends on how you want to model your problem, and, how you interpret the answer. Let's say your treatment is a parameter. The bayesian approach won't tell you what that parameter is, but will provide static confidence intervals of where it lies. More data, and informative priors will change the shape of this distribution. The frequentist approach will tell you the parameter (the treatment), with variable levels of confidence (depending on the data).
I am completely new to this concept but came down as a Bayesian thinker. I immediately thought however that my acceptance of uncertainty and willingness to make decisions even knowing the uncertainty is an unusual quality in me. It tends to drive others nuts as they prefer to be certain before acting. I guess I simply think certainty is an illusion most of the time. And I would definitely say that about medical risks as the research quality is often so poor or misunderstood or out of date and so on. Are you familiar with Ben Goldacre? If not please check his UA-cam lectures.
49% heads. - 49% tails - 0.4% a bird steals it - 0.4% it disappears - 0.2% I’m imagining this and it doesn’t exist (but my eyes construct the visual spectrum in my mind)
I think it has a lot to do with the nature of the question and the search-space in your problem, rather than your personal choice, to go with a frequentist vs bayesian method.
I don't think the framing of Frequentists caring about the true answer is a good one. Bayesians and Frequentists both care about truth, they just care about the true answer to different questions. I think the main difference is that Bayesians and Frequentists ask different questions, and use language that implies the questions they care about, which is what makes it so difficult to have a conversation with the other perspective. When truly asking the same question, the two mindsets should converge on the same answer.
The main difference is how probability is defined. For Bayesians, probability is one's degree of belief. So, it is inherently subjective. For frequentists, probability is a law of the universe that regulates an event's long-term frequency of occuring. So, it's opposite of subjective. All the other differences stem from this one.
Very much agree. Wittgenstein would say: arguing for one, against the other, is simply an abuse of language. There is no contradiction. One is not right, while the other is wrong. Those that argue are misled by their own language use. Language is highly indeterminate. "What side is up?" Sounds like a simple and straightforward question, but it is not. It is based on context, the forms of life, and family resemblances. To the question, "what is the chance it is head's up?", it can be interpreted as in what is the chance your guess is correct, or what is the chance the actual state is head's up. In a deterministic universe, the frequentist would not even be able to say there is a 50% chance it lands head's up before the coin has landed. It may not have landed, but how it will land is determined by prior values that have already been set in motion.
I agree with banana's comment. For example when I read about zodiac signs, it usually describes the signs strengths and weaknesses. But I've always wondered how can someone who is not of that particular zodiac sign classify or identify a sign's attributes as a weakness? This assumption would imply that you've lived through their experiences.
If we say for Frequentists the probability of a system is a 'property of the Universe', a property of the system. Then Baysians allow talk about their belief of that probability, whereas Frequentists restrict themselves to estimates of the probability to calculations on the data. ?
@@cpmathews2566 You have no concept of the collective. As a collective it was what she said it was both for you and her because we all see the same colors on the rainbow. This schrodinger's cat thing is such a bas tardization of the scientific method and everything that has made progress in science up until that dumb concept came about. It's literally not true. The nature of statistics itself is that we can't determine something or its nature. Schrodinger took the nature of statistics itself and masked physical phenomenon with it and said "this is the fundamental nature of the universe" when the entire time it was relative to us and our ability to know. So statistics and its nature is schrodinger's cat we'll say but not the universe. You may be confused but the universe is certain.
It seems like it first depends on how a person understands the initial question. I understood it as what's the probability of me guessing if it was heads or tails. Answer is always going to be 50/50. The coin already landed so it was never a question of which way it was resting on your palm. That has already been determined. The only thing left to do is guess the right answer...which is always going to be 50/50. Edit: This was such a random video click for me. Lol.
This is how I understood it as well. It seems kinda flawed, in a way. Is the way of determining whether you are Bayesian or Frequentist examining how you interpret implications in the question? As I stated in another reply, the question, as I believe is likely to be understood by most, would be "What is the probability [that you could correctly guess] that this coin is heads-up on my palm?" Or is the video saying that Bayensians would assume that she is referring to the guess and Frequentists won't? If that's the case, then Frequentists don't sound very fun at parties... I feel like this determines more about how wiling you are to "go along" with a potentially unclear question. I think, in a more casual setting, a Frequentist is still likely to guess 50% because, in their mind, they are going along with the commonly understood implication of the question, or, in other terms, "trying not to be a smart-ass." Is this psychology or statistics or both?
This is a fantastic short explanation of the differences between them - thank you! Also, for some reason, you kind of remind me of Kes from Star Trek Voyager…
@@6400ab wasn't it obvious what 'on' was used here for? Sit on the chair. Anyway, leave it. We are going into ambiguous linguistic terminology which is completely missing the point of this whole discussion.
I think it’s important to understand whether your need is action - doing or not doing something in the real world - or just thought/academic. Bayesian tends to promote action, such as our decision to drive more slowly in poor weather. Frequentist tends toward addressing issues where a discrete level of certainty has utility (often without action), such as hypothesis testing.
If you can't provide an exact response, you're not interested in the truth. Frequentists can easily extrapolate based on past experiences while Bayesians would have a very hard time modeling those very same deterministic events. Let's say you succeed, and you manage to model every possibly deterministic event within your Bayesian model... Guess what, it's now a frequentist model!
01:00 Why did you look at the coin half-way through asking the question? The act of looking might change the results for some of the audience; so do they answer before you looked, or after you looked? The Bayesian probability of course changes for you; but to some extent changes for the audience, as they've see your reaction and thus received non-zero information about the true state of the coin.
1:00 I thought it was a trick question and you were going to show the coin stading up, stuck between your fingers, to make a point about how there might not be a probability. Guess that makes me a Bayesian.
Is it possible to be a frequentist before the coin is flipped, like the answer of that coin landing heads or tails is already 100% or 0% which is predetermined by a multitude of factors such as its orientation at the moment, how hard you will flip it and so on, all of which are all also pre-determined but we just don’t know them
Thanks for summarizing this important topic. I've no emotional investment in the Frequentist vs Bayesian debate (I've used both often in my research), but I couldn't help but feel the Bayesian perspective was not given fair credit here. The Bayesian's "point of view" should not be entirely subjective, but rather based on logical principles, that can often be derived from the laws of nature (eg. The shape and symmetry of the coin make it equiprobable to land on heads or tails). The powerful advantage of leveraging prior information for forecasting or evaluating hypotheses also ought to be emphasized more. Ideally, aspects of both Bayes theorem and frequencies should be used (eg. using base rates as prior information in diagnostics). But because the frequentist approach is so much more intuitive to use in science, the Bayesian approach is underutilized. This has been less than optimal for science which has been far too dogmatic about p-values instead. It would be nice if you could emphasize this more in future communications on this topic, thanks!
If the coin is heads-up before tossing, it will always land heads-up, and vice-versa, IF it's landing on the palm of the person tossing the coin. If it's landing on hard surface, it can go anywhere due to the bounce / twist / turn of the coin multiple times before it comes to rest. So, which one am I?
Forgive my stupid question (which might be slightly off-topic), but doesn't it matter which side is facing up before the flip, how the coin is placed on the thumb, how much force it used for the flip, and some other factors (which may or may not be negligible)?
I'm backing the superposition, where the superposition changes based on the likelihood that you were lying in the reveal, since the coin was too out of focus to tell what the result was.
But when we talk about Bayesians view, then one would need to mention Bayesian networks. And those shall rather be compared with the coin example. Because in Bayesian Nets you would actually construct a graph with a node saying "coin was flipped" and then dealing with the probability of the coin being flipped. That's were also the strengths of a BN approach lie. When you would need to narrow down in a (short) amount of events that certainly influence the outcome. So each approach heavly relies on the hypothesis to test. The more unknown factors you have the more you tend towards a frequentists view. Right?
why is this a debate? if you have to make decisions with limited info, ie not knowing the data set (such as not having any more information prior to or after the coin flip) then you have to be Bayesian. If you know the data set, or if you're answering a silly question like "whats the probability that the coin has landed on the side that it has landed, no matter which one" then you have to be frequentist. If you wanna be technical, then frequentists have to be frequentists about all possibilities for every event, since given determinism all the coins HAVE in a sense, landed. But that's not useful from our perspective, so a lot of the time they have to be bayesian. I just don't see the debate, bayesianism and frequentism answer different questions, and which question is right to ask depends on the circumstance
The Baeysian recognizes that the probability is relative to perspective which means recognizing the context of other's perspevtive. Perspective must involve uncertainty. The problem is that it usually loses that component. I think some people combine the two to eliminate their feeling of discomfort.
Holy crap, statistics has a place for me. Never heard of Bayesian before. I gotta do some reading now. Thank you! Seriously, that makes so much sense in my world.
Now I'm even more confused. Before the coin toss I thought that the probability of the coin landing head up was 50%. After the coin landed, it was now my chance to guess its landing side correctly to become 50% (since its landing side was already decided). Sooo, am I a frequentist?
If you are a frequentist, when the coin is landed, you will say it is either 0% or 100% (no longer a probability). But, if you are still thinking of your probability becomes 50% higher to be correct, meaning that you still think of a 'point of view' and a probability, in my opinion, this means (correct me if I'm wrong) that you think in a bayesian perspective
I first answered 50%, then thought about it while she was peeking at the coin and said: 100%. Then thought about it a bit more and said: Meh, I have no idea. What does that make me?
Then you are an Bayesian. Why? A Frequenists would have answered "Frequenists" and then measure how often they were wrong. You want to guess right and therefore say both (just like a Bayesian does with the coin)
Thank You.. You are a seriously great teacher, I'd like to see your videos as a necessary part of every high school students curriculum. You remove the jargon and re-frame the learning references to simple, understandable examples which makes the learning of complex issues so much easier.
please explain: so, from a bayesian perspective, yes the coin has already landed, but the core of the question is what was the probability of it having landed on heads or tails? it can only ever be one of two twings, yes or no, blue or red, up or down, always 50% to be or not to be.
what is the 'validity' of the question about probability of heads or tail once it is landed in your palm in this example is not clear ? what are its implications ?
The way I thought of it was that the chance that an event did/can/will happen is actually always either 100% or 0% and it is just a lack of knowledge that makes it appear otherwise. Or in other words, probability is like a measurement of our own ignorance (are we slightly unsure or very unsure? etc). I don't know if that shit's true, it just looks like it to me.
it occurs to me that most situations where you want to know a probability are Frequentist, i.e. they concern things that are already facts, but unknown to us. From a certain perspective *all* probabilities are Frequentist, if you accept that we live in a deterministic universe. All future tosses of the coin are already predetermined! Love this post!
Cassie, thank you for detailed explanation. Please, please, please tell us more about pros and cons of Bayesian vs Frequentist approaches in the business context.
3:11 "What is the probability this coin is up heads?" Still 50%, there is apparently a third category I am part of. Or more likely the perceived dichotomy isn't one.
So, if I was to try and put that in terms I’ve spent some time with, I’d say: A Bayesian attempt at ‘finding truth in uncertainty’/‘making predictions’ finds base rates relevant. So we cultivate relevance around the coin only landing on heads or tails, but do not place relevance on the physics of the coins’ trajectory and inertia, physical determinence, interaction with air molecules, etc etc. We use base rates as an end, and not a means to an end. A Frequentist will cultivate relevance of those latter things, as they claim we shall assert we live in a determined universe, but in so far as we cannot fully gasp all the elements of that determination, we can use statistical models instead and judge their efficacy from the outcomes. Is that right?
Hm, I'm wondering whether I can say this?: 1) Frequentist statistic is an inductive approach - trying to infer properties of the population from collected data (which also includes evaluating the assumptions of properties of the population by analysing the likelihoods of data given these assumptions --> see significance testing). 2) Probability is deductive - "knowing" properties of the population and inferring properties (probabilities) of data points from that. (And Bayes specifically includes Beliefs, which can be updated). P.S. I'm not sure how to handle the concepts probability and Bayes - are they the same or is Bayes a special case of probability or ...?
What's the frequentist perspective on getting the model right? It always seemed to be like bayseans try to make that more explicit but I struggle to see a real distinction, but I'm kind of convinced (after adjusting my prior ;-) I just don't understand the semantic distinction that the frequentist perspective had with respect to (implicit) assumptions
Thank you for the simple explanation :) As far as I understand, the frequentist statistics is correct. However, from my point of view as a research scientist, the frequentist statistics is often irrelevant! Because I am often interested to know if my model or explanation of a complicated reality is consistent with the observations. These types of questions are consistently addressed within the framework of Bayesian statistics. On the other hand, the Bayesian approach is still missing an important ingredient. Bayesians still do not agree on how to construct priors! How does one construct a prior, which represents one's knowledge?
As a kid, I used to wonder what the space between the stove and the pot was called. As an adult, I had the same issue with frequentism, I just didn't know how to formulate the question.
For that example I got Bayes. From my perspective, the coin is in an eternal state of 50/50. Until it is observed. Like quantum physics, What matters is the observation. Until I can see it, the coin is 50/50. I would say: it is just as likely to be heads up before or after the throw.
What if you make an x-ray and can see through the hand that it`s heads? Is the probability still 50/50 before you raise your hand and "see it" youth your own eyes?
@@thebrutaltooth1506 Assuming the x-ray is working correctly and it could show me that. *Yes* Because I observed it. In my opinion, an observation is any kind of measurement or reception of information through any way possible. e.g. tests, touch, etc. Evolutionary theory is based on this. We don't directly observe any of that information.
@@Lucas747G Interesting, I can respect that. Don`t know what you mean about the evolutionary theory though. You can directly observe evolution but by looking at the canges in a population not of an individual. "The English moth, Biston betularia, is a frequently cited example of observed evolution. In this moth there are two color morphs, light and dark (typica and carbonaria). H. Kettlewell found that dark moths constituted less than 2% of the population prior to 1848. Then, the frequency of the dark morph began to increase. By 1898, the 95% of the moths in Manchester and other highly industrialized areas were of the dark type, their frequency was less in rural areas. The moth population changed from mostly light colored moths to mostly dark colored moths. The moths' color was primarily determined by a single gene. So, the change in frequency of dark colored moths represented a change in the gene pool. This change was, by definition, evolution." (Source:abyss.uoregon.edu/~js/21st_century_science/lectures/lec09.html)
Frequentist: "What is the probability the actual current state of the coin is ..."? Bayesian: "What is the probability my estimate of the state of the coin is ..."? It seems Frequentists try to take an objective point of view. Meaning: from the perspective of the focal object. Whereas the Bayesians take a subjective view. Meaning: from the perspective of the subject/observer.
The explanation of frequentist thinking in the video sits uneasily with me. The idea that a flipped, but hidden, coin would be either 0% or 100% (but unknown) while an unflipped coin would be 50%, or a coin flipped and waiting to land would be 50% seems arbitrary. It's more subjective than the Bayesian explanation in a way! There are a number of reasons why the outcome might be obscured to us, whether that data is temporally obscured (you have't flipped it yet, and we experience time in one direction!), or physically obscured (a hand is in the way), or obscured through laziness (the flipped coin is in the air waiting to land and we could measure the rotation and velocity and calculate how it will spin and drop and land, but we don't bother). I don't see, on an ideological level, why it should make a difference which of these it is. So if the hidden coin is "either 0% or 100% but I don't know which" to a frequentist, why not the future event coin too? It seems that there is something getting lost in the difference between the questions: "What side *will* this coin land?" and "What side *did* this coin land?" The frequentist as described here doesn't ever change their answer to the first question once the coin has flipped, they just start answering a different question instead, right? As I far off the mark if I were to think that maybe a change in information is being acknowledged in one case explicitly by changing the answer and in the other case implicitly by changing the question?
@@zak3744 You are correct in many things you say. In a deterministic view, everything is already determined. So, to a Frequentist this would have to mean that all coins being flipped, either in the future or past, all are determined ... and thus none have a probability. Only abstracted coins have probabilities in this sense. Elsewhere here, I commented about this being really a linguistic difference. The difference is not really about the understanding of reality, but what question is asked. Usually in science the Frequentist question tends to make most sense. It is about the object / objective reality. When you look at it from a decision making agent, it makes sense to look at it from a Bayesian perspective. The question is then about: what is my best estimate based on what I know? Or: the best decision based on the information available to the Agent (e.g., a robot).
So, is there a problem in statistical analysis where a Bayesian and a Frequentist would come up with different, empirically distinguishable answers? And if so, which answer would turn out to be correct?
It's important to note that frequentist theory is an incomplete theory. Bayesian inference is a theory that represents reality better -- with more accuracy. It addresses uncertainty, for any state of knowledge. It's also important to note that frequentists try to estimate a parameter (point/range estimate) for something. Bayesians try to evaluate degrees of plausibilities among hypotheses for a specific parameter. These are two different approaches to the problem of trying to figure out what the parameter is. Therefore the interpretations of them are also different!
If the frequentist has a predisposed action that they like to take in a situation, does that not equal to their belief, which in turn means they are using their previous belief to take an action and update their beliefs making it Bayesian?
The problem with this test is that it has no implication. The person on the other side of the table forms opinion but does he act differently? With your coin-tossing example if there are one Baysian and one Frequentist on the other side of the table and they want to engage with you in a game of chance are they going to bet differently on a coin that you have already tossed? A better example would be for you to toss a coin once and show the income to One Baysian and One Frequentis. The outcome is Head. Then you ask them to bet on the next income to be Head. What odds the Baysian and Frequentis would agree to?
This is a finely done video - props to Kozyrkov for a superb presentation. I think, however, the emphasis on the subjectivity of Bayesian inference is a bit misleading. One comes away with the notion that frequentists are interested in reality while Bayesians are interested in opinions. Surely all practitioners of data-based inference are interested in reality; the difference lies in kinds of questions by which reality is sussed out. The Bayesian and the frequentist might agree that a given state or process in the world can be understood in terms of definite parameters, i.e. that the flipped coin has already landed. To say that the Bayesian approach is subjective is simply to say that it is concerned with *our knowledge* - or, equivalently, our *uncertainty* - regarding the parameters of interest given available evidence (data + priors). I suppose this could be called "subjective" since it depends on the knowledge available to a subject, but it is certainly not subjective in the pejorative sense of "arbitrary." In most cases, at least in my field of ecology, the frequentist is also interested in parameter states. That, after all, is what it means when we ask whether X causes Y. But frequentist methods get there indirectly by inferring the likelihood of evidence (data only, no priors) given assumed parameter states. While these approaches generate parameter estimates (parameter values that maximize the likellihood of the data) with uncertainty (intervals that would contain the true parameter value in X% of hypothetical repetitions of the sampling and analysis process), they do not tell us directly what we really want to know: what should we believe about the unknown state of the paramater? This is what we want to *know* because it guides what we want to *do*, i.e. to understand and potentially intervene in the world. These objectives, like our knowledge, are intrinsically subjective, but in a sense that is both legitimate and unavoidable. I also think it is a mistake - not one made explicitly by Kozyrkov, but one occasionally suggested by others - to project approaches to data-based inference onto metaphysics. Choosing between frequentist and Bayesian methodologies should have nothing to do with whether one is an ontological realist or nominalist. As Andrew Gelman puts it, "theoretical statistics is the theory of applies statistics." Pragmatic handling of uncertainty, appropriate to the question at hand, is the only end for which statistics is a legitimate means.
Take the coin flip as done and in her hand unseen. Now suppose you have to make a decision which will result in your death if you get it wrong (or some equally bad out come). Which approach will give you the most reasonable model ?
just came across this wonderful video, very simple explanation, read many articles but still confuse with the technical terminologies they have used in the paper. from this video within 5 minutes i have understood the concept. Thankyou Cassie for sharing wonderful knowledge with us. really appreciate it :)
I kind of understand, a frequentist sounds like they care about what is "possible", if there are two possible options, like heads or tails and an event which has a before and an after. Before the event we can consider those 2 possibilities. After the event we can consider the outcome but there is no possibilities to consider, as one them was realised. If you have been taking prior beliefs and outcomes into account then you would have something to consider.
Really makes me think of the Monty Hall problem, because that hinges on the fact that Monty Hall has more information than you do -- just like Cassie looking at the coin while we don't see it. Is the conclusion that you should switch doors in the Monty Hall problem based on Bayesian or Frequentist analysis? Or is there a case to be made using either?
For me, Bayesian. With Bayesian, your own knowledge affects the probabilities you calculate for yourself. You can add information to your calculation and adjust your personal estimates. With standard Monty hall, you pick a door and calculate 33% chance of winning. Monty opens one door and the one that was neither opened nor chosen now has a 66% chance of being the winner. The one you chose still only has a 33% chance of being the winner, so switch. But now the twist. Imagine, at this point, a second contestant walks in and is also given the choice of one of the two doors. They see the exact thing you do, two closed doors and one open. But being late to the party, they will only have a 50% chance of picking the winning door compared to your 66%. Bayesian can easily handle this. Can a frequentist view reflect these simultaneous yet differing odds. Maybe someone could show us how a frequentist would handle this shift in odds based upon personal knowledge?
You seem to be assuming that each one is not useful in different circumstances both are useful depending on what is knowable and what you plan on doing next.
I don't know anything about statistics, but it sounds like when each group answers the "what probability is it that it's x?" question, they're focused on two different referents. The frequentists interpret the question as referring to the actual, determinate state of affairs in the world, while the Bayseians interpret it as an epistemological question, that is as a question about our knowledge. Two ways of interpreting what "probability" refers to.
I saw a different video on confidence vs credible intervals. This was my comment: The long run performance of the 'ensemble' of intervals is what gives us confidence the observed interval indeed covers the true value. We can therefore say we are 95% confident the observed interval indeed covers the true parameter. It is nonsensical to consider the population level parameter as an unrealized or unobservable realization of a random variable that depends on the observed data just so we can make philosophical probability statements about the parameter. Unless the parameter was sampled with replacement from the prior distribution and a new value sampled from the posterior, it is absurd to attribute posterior probability statements to the parameter. While the p-value is typically not interpreted in the same manner, it does show us the plausibility of a hypothesis given the data. It is the inversion of a hypothesis test that gives rise to the confidence interval. See confidence distributions, confidence curves, and confidence densities.
I am thinking about how this would apply to political polling and election simulations. I'm not sure how i would use this information to help me there...
From what I know, vote polling usually uses a Frequentist approach (notice that they almost always have a margin of error attached, which is a concept from the frequentist framework).
Clear explanation, thanks. Will it be possible to have a mathematical explanation as well, such as doing the same analysis (for instance comparing mean across two groups) using Frequentist (a t-test) versus Bayesian approach (?) ?
I think I miss somewhere the point. Is the question about the occurence of a thing under uncertainty? But then I understand the Bayesian as a theory about all occurences [because (s)he starts already with a theory] (of a certain kind of thing) under uncertainty. So (s)he would say: in the end, if you look at the data and your hypotheses then there is a 50% probability that either head or tail. But the frequentiast would look only for this single occurence. This single occurence can only have one truth value either head or tail. So either his/her guess is wrong or right. But in the end, if the frequentist would make enough coin tosses (s)he would likely progressingly (?) to come to the hypothese that from all coin tosses, half of them is head, half of them is tail. So they would share the same opinion about the distribution of heads or tails.
And at least Bayesian willing to admit its' own bias. Frequentist on the other hand makes assumption without consideration. As a result, Bayesian helps the field of ML alot and Frequentist doesn't.
Pretty bold to consider a whole area to be useless. All models have limitations and like anything other thing, when frequentist statistics is done correctly, it can be useful
I love this.. However, you ask the question, what is the probability the coin is heads up on my palm? My answer is 100%, as you have both palms touching the coin, therefore it is 100% probability the coin is heads up and tails up on your palm. Does that thought process make me a Bayesian or Frequentist?
I am kinda confused as well... The implication of a question like that tends to be "What is the probability [that you could correctly guess] that this coin is heads-up on my palm?" Because, in a situation where you aren't taking everything as directly stated, like a casual conversation, I would say, and I would assume most would say, "It's 50%." But if the question was asked more directly, making sure to directly state that she is asking the probability of the coin's state itself and not your guess of it, then I believe that most would have a Frequentist response.
PsiGreen Thats perfectly right, BUT only when you don’t care about the outcome. See, If you know its a Head, then you wont be using probability. If you are to guess we arrive at 0.5. If you don’t wanna look or guess then why do the whole bloody experiment? Its a moot point really.
Can someone give me a nontrivial example of a good frequentist approach as we almost never actually know the probability of an outcome or are blindsided by an outcome we never even anticipated.
With clearly defined axioms/system, Bayesians are the objective ones and frequentists are the subjective ones, being led by statistics of a data sample. Am I claiming this opinion of mine is true because I am a Bayesian?
I'm trying to do Bayesian inference where the prior and likelihood distributions are Cauchy distributions. Can you (or anyone else) point me in the direction of how to do that? There are lots of resources online of how to do Bayesian inference with normal distributions and beta and gamma distributions, but I don't see anything involving Cauchy distributions.
I am not sure I really got the difference (I know nothing about the subject): "The frequentist will say there is a 0% or 100% chance, but I don't know the answer." Fine, but there is a 50% chance of your guessing it correctly. Therefore, the Bayesian is simply skipping a step and merging the 50% chance of guessing correctly with the chance of the coin falling heads or tails. So, in reality: a) before you toss the coin, (i) there is a 50% chance of being heads or tails; (ii) you have a 50% chance of guessing if it is heads or tails; b) once the coin has landed and you can't see it yet, you still have a 50% chance of guessing it correctly; c) scenario (b) is the exact same as if you guessed before the coin was tossed and nobody hid the result (like in sports matches when they fall to the field/court). Your guessing chances don't change on whether the event has already happened. If the result is not revealed, you still have a 50% guessing chance no matter what. Because your guessing doesn't influence the result, both perspectives are reaching the correct answer, but only highlighting different parts of it. Maybe I am taking the example to literally, but it does not sound to me like two conflicting viewpoints.
"opinion" vs "no opinion" ! But what about the "opinion"/metric on what the Frequentist's methods quality is aka "what is the lower threshold of 'good enough' " ?
It's curious to think about probability and statistics theories in physics. In my perspective, the experimental physicists generally goes with a Frequentist mind, since the common mindset is to try the same experiment over and over and look what percentage they got a "good answer". In the other hand , the theorists care too much about perspective and information, actually the quantum theory is bounded to theses concepts, hence, the resolutions of the problems are made from a Bayesian mind. Your videos are awesome! Loved it!
Statistical probability is a measure of ignorance, not certainty. Everything that Does happen always had a 100% chance of happening, we just didn't have enough information to know it. The two perspectives are perfectly compatible. Also, knowledge is justified belief.
Agree on the first bit, but not on the second. Knowledge is not simply justified belief, some does occur that way but much is also direct knowledge that does not require a belief.
There is no such thing as rigid distinction between the two, I use both, just not for the same reasons obviously. Why would you choose only one anyway? There isn't a better one, so don't choose, both are important, and both can be very useful to consider in a same situation to see different things, it helps resolve problems in (unusual sometimes but) effective ways. I'm just gonna leave it here but if rings any bell to somebody: I try to never be content with my deductions or ways of seeing and conceiving things, so I try to force myself to see from perspectives where I'm always wrong, even if it's from stupid reasoning/perspectives, it helps see unexpected things and patterns sometimes where we expect them the least and it drastically help understanding notions of relativity.
I love this subject! I'm studying Bayesian methods in my PhD, here's my perspective:
Frequentist reasoning wants to deal objectively with data, so it considers probability to be a property of the world; it says "the coin has probability 1/2 of being heads because that's the frequency of heads in the behavior of this coin"... and there's a right probability, it's a fact from the world, it can be learned by data that shows that frequency in behavior. Data is noisy, but it reveals true propensities through frequencies.
Bayesian reasoning wants to deal logically with data, so it considers probability to be a property of logical propositions about the world; it says "the statement 'coin landed heads' has a certain probability of being true, it is 1/2 for me and 0 or 1 for you depending on what you see"... the proposition is connected to a point of view, and different points of view will differ in how close they are to the truth about the state of the coin. So probability is subjective in a sense, but all points of view with equal information should objectively agree about probabilities of their statements (it's objectively subjective, just recognizing the existence of different points of view, but they are not supposed to be personal, not opinions). When you update your "belief" over data, it's because data moved your point of view in relation to the "truth". In this example, once we see the coin, we update the statement "coin landed heads" from 1/2 to 0 or 1 depending on what we see (probabilities of 0 and 1 mean perfect information while 1/2 means no information).
There isn't an actual divide between the two, theoretically... Bayesian reasoning recognizes the relation between frequency and plausibility, while frequentist reasoning recognizes points of view, it just doesn't go there.
So in other words the frequentists approach will give you a correct answer every time but may need indefinitely to evaluate, while the bayesian approach gives you a result immediately but this result may be wrong.
@@ndrsvgl hm... the approaches are answering different questions, both correctly... what is this answer/result that you say they are trying to give?
in the experiment of the coin, we can arrange for the mutual agreement of the two approaches in every observable event (observable in the sense that it doesn't talk about probabilities)... for example, if you flip the coin and ask for the exact result it will give, both should agree in saying: "I can't tell"... if you say you flipped the coin a zillion times and aks for the proportion of heads, both should say immediately: "it's 1/2" (but they would interpret your question differently)...
I guess you are talking about this difference: you ask what is the probability of you having a coin in your pocket. One bayesian could say: "I know nothing, so for me it is 1/2"... another bayesian could say: "I saw you handling coins before, and if I have a model for how probable it is for "coin handlers" to have coins in their pockets, I can update that probability of 1/2"... another bayesian could say: "I know that people in this city carry coins in their pockets with a chance of 30%, so it's 30%"... someone could say: "it is 80%, because I saw in the stars", but that wouldn't be bayesian, it's a personal kind of subjectivity... a frequentist would say: "i can't know, because I don't know anything related to the frequencies with which you carry coins in your pocket, i don't talk about probabilities for single events"
now, those bayesians can't be right at the same time, yes? and that frequentist will take a long time to discover the frequency by making the situation become a repeatable experiment... the thing is, all bayesians are right, but their answers have limited power where the frequentist has no answers at all... it may seem silly, but that "imprecise" reasoning of bayesians has major applications, here's a very understandable example: en.wikipedia.org/wiki/Bayesian_search_theory
Bayesian and Frequentist are two thinking methods to answer different questions: what I know and what I should know. None are wrong, and it doesn't have to do with psychology or personality. It depends on the situation and which question should be answered first.
@@lrgui9792@N73B60 Ok, thanks for clarification.
My interpretation is that the bayesian reasoning is correct, but the frequentist reasoning is easier for a variety of reasons so scientists often use it instead. I take this comment as empirical evidence for my claim, as the frequentist explanation takes about 1/3 of the words to explain than the bayesian.
As a psychiatrist, I feel like I rely on both Bayesian and Frequentist philosophies in my everyday work. When advising on diagnoses, I use the Bayesian approach. That is, I gather whatever data I can to inform an opinion (about a diagnosis), and then I update my opinion if and when more data emerges. I'm not overly invested in getting a 'right' diagnosis because a patient's presentation is dynamic and complex such that they can't always be reduced to a single category at all times. I'm happy to revise the diagnosis when necessary.
But when I'm advising on risks (i.e. the risk of somebody committing suicide, homicide, arson, etc.), I use the Frequentist approach. I am infinitely more concerned about what will happen when a patient has had numerous repeated attempts at harming themselves or others because that informs the probability of how likely a person is going to repeat history. I think to myself, "what will happen if the patient attempts the same move another 100 times?"
To me (and I'm not a statistician, although I know a little about human psychology), the Bayesian and Frequentist approaches are fundamentally concerned with certainty vs uncertainty. The Bayesian aligns herself with changeable opinions informed by available data, thus she is never completely 'certain' about anything since her opinions change when new data emerges. The Frequentist on the hand aligns himself with unchangeable facts based on logic, thus he is always completely 'certain' about everything as long as his logic holds water.
The coin toss was a great teaching example. It was a great example because the answer was inconsequential. I mean... Who cares how the coin lands? Nobody was harmed in the making of the video, yes? (I hope). We can allow ourselves to assign equal weight to both philosophies in this teaching scenario when the outcome of the coin toss was inconsequential.
I suspect people are likely to gravitate towards a Frequentist approach when contemplating decisions that are very consequential because the Frequentist approach feels more tangible to me while the Bayesian approach feels more abstract.
So I don't think it is a matter of 'are you a Bayesian at heart or are you a Frequentist?' Rather, it may depend on the weight of the decision you are about to make. Having said that, I do acknowledge that some people are more tolerant of uncertainty than others, thus for those people, they are more likely to be Bayesian perhaps.
Does this make sense?
It's less about the weight of the decision but the fundamental structure of the question. If you ask, "What is the probability I WILL flip a coin heads?" versus "What is the probability this is heads?" then this is the difference between the two thoughts and it doesn't matter the importance or the pertinence or the weight. So you are right in saying it has nothing to do with personality or thought process its just whether or not people are aware about the two different "modes" if you will of an outcome.
Do not mix human senses with the math. Both Bayesian and Frequentist approaches are mathematically solid and they converge when infinite data is available. F. put the uncertainty into sampling, i.e. we do not know the exact value because we only observe a limited subset of the universe and we can make an estimate of the interval where the true value can be. B. put the uncertainty in the value itself: as we have limited data available (including prior knowledge) we can say that the value in question can be drawn from a distribution. So instead of a point estimate B. give you a distribution of values. There is no more correct or less correct approach, it depends on what you want.
I like this approach! It definitely depends on how you want to model your problem, and, how you interpret the answer. Let's say your treatment is a parameter. The bayesian approach won't tell you what that parameter is, but will provide static confidence intervals of where it lies. More data, and informative priors will change the shape of this distribution. The frequentist approach will tell you the parameter (the treatment), with variable levels of confidence (depending on the data).
I am completely new to this concept but came down as a Bayesian thinker. I immediately thought however that my acceptance of uncertainty and willingness to make decisions even knowing the uncertainty is an unusual quality in me. It tends to drive others nuts as they prefer to be certain before acting. I guess I simply think certainty is an illusion most of the time. And I would definitely say that about medical risks as the research quality is often so poor or misunderstood or out of date and so on. Are you familiar with Ben Goldacre? If not please check his UA-cam lectures.
Psychiatry is GAY.
49% heads. - 49% tails - 0.4% a bird steals it - 0.4% it disappears - 0.2% I’m imagining this and it doesn’t exist (but my eyes construct the visual spectrum in my mind)
I think it has a lot to do with the nature of the question and the search-space in your problem, rather than your personal choice, to go with a frequentist vs bayesian method.
Exactly
I don't think the framing of Frequentists caring about the true answer is a good one. Bayesians and Frequentists both care about truth, they just care about the true answer to different questions.
I think the main difference is that Bayesians and Frequentists ask different questions, and use language that implies the questions they care about, which is what makes it so difficult to have a conversation with the other perspective. When truly asking the same question, the two mindsets should converge on the same answer.
The main difference is how probability is defined. For Bayesians, probability is one's degree of belief. So, it is inherently subjective. For frequentists, probability is a law of the universe that regulates an event's long-term frequency of occuring. So, it's opposite of subjective. All the other differences stem from this one.
Very much agree. Wittgenstein would say: arguing for one, against the other, is simply an abuse of language. There is no contradiction. One is not right, while the other is wrong. Those that argue are misled by their own language use. Language is highly indeterminate. "What side is up?" Sounds like a simple and straightforward question, but it is not. It is based on context, the forms of life, and family resemblances. To the question, "what is the chance it is head's up?", it can be interpreted as in what is the chance your guess is correct, or what is the chance the actual state is head's up.
In a deterministic universe, the frequentist would not even be able to say there is a 50% chance it lands head's up before the coin has landed. It may not have landed, but how it will land is determined by prior values that have already been set in motion.
I agree with banana's comment. For example when I read about zodiac signs, it usually describes the signs strengths and weaknesses.
But I've always wondered how can someone who is not of that particular zodiac sign classify or identify a sign's attributes as a weakness? This assumption would imply that you've lived through their experiences.
P.S. they're trying to raise robots. I think it's in a Disney movie "Inside Out"
If we say for Frequentists the probability of a system is a 'property of the Universe', a property of the system. Then Baysians allow talk about their belief of that probability, whereas Frequentists restrict themselves to estimates of the probability to calculations on the data. ?
LOL. Schroedinger's coin.
Not only Schrödinger's coin, at 50/50; But when she showed us the coin I could not see it clearly. For me it is still, 50/50. Fore her it's 100%
@@cpmathews2566 You have no concept of the collective. As a collective it was what she said it was both for you and her because we all see the same colors on the rainbow. This schrodinger's cat thing is such a bas tardization of the scientific method and everything that has made progress in science up until that dumb concept came about. It's literally not true. The nature of statistics itself is that we can't determine something or its nature. Schrodinger took the nature of statistics itself and masked physical phenomenon with it and said "this is the fundamental nature of the universe" when the entire time it was relative to us and our ability to know. So statistics and its nature is schrodinger's cat we'll say but not the universe. You may be confused but the universe is certain.
@@traininggrounds9450 relax. quantum bayesianism is a thing. just has its own limitations with locality etc etc.
Hilarious
What is the chances the coin is not there in her hand ?
Two minutes in to my first Cassie Kozyrkov video and I'm subscribed.
Me too!
Hidden under your other hand or hidden in the future, is there a meaningful difference?
It seems like it first depends on how a person understands the initial question. I understood it as what's the probability of me guessing if it was heads or tails. Answer is always going to be 50/50. The coin already landed so it was never a question of which way it was resting on your palm. That has already been determined. The only thing left to do is guess the right answer...which is always going to be 50/50.
Edit: This was such a random video click for me. Lol.
This is how I understood it as well. It seems kinda flawed, in a way. Is the way of determining whether you are Bayesian or Frequentist examining how you interpret implications in the question? As I stated in another reply, the question, as I believe is likely to be understood by most, would be "What is the probability [that you could correctly guess] that this coin is heads-up on my palm?" Or is the video saying that Bayensians would assume that she is referring to the guess and Frequentists won't? If that's the case, then Frequentists don't sound very fun at parties...
I feel like this determines more about how wiling you are to "go along" with a potentially unclear question. I think, in a more casual setting, a Frequentist is still likely to guess 50% because, in their mind, they are going along with the commonly understood implication of the question, or, in other terms, "trying not to be a smart-ass."
Is this psychology or statistics or both?
I agree. I had to watch it again because it made no sense to me! Her metaphor / analogy / example is poor.
This is a fantastic short explanation of the differences between them - thank you!
Also, for some reason, you kind of remind me of Kes from Star Trek Voyager…
0:56 "... heads up on my palm" ... ... which palm?
Yeah, I guess 100% based on the fact that there was a palm at the ready for each side.
And who should the palm belong to?
*on* my palm, not below my palm
@@kartikkalia01 "on" =\= "above"
@@6400ab wasn't it obvious what 'on' was used here for?
Sit on the chair.
Anyway, leave it. We are going into ambiguous linguistic terminology which is completely missing the point of this whole discussion.
I think it’s important to understand whether your need is action - doing or not doing something in the real world - or just thought/academic. Bayesian tends to promote action, such as our decision to drive more slowly in poor weather. Frequentist tends toward addressing issues where a discrete level of certainty has utility (often without action), such as hypothesis testing.
Your action vs action recommended as an expert interpreting data?
*Neo* "Heads!"
*Morpheus* - "What if I told you there was no coin...?"
A better question is, would you go for Monte Carlo simulations or bootstrap draws for small samples 😉
and what if I do both?
If you can't provide an exact response, you're not interested in the truth. Frequentists can easily extrapolate based on past experiences while Bayesians would have a very hard time modeling those very same deterministic events. Let's say you succeed, and you manage to model every possibly deterministic event within your Bayesian model... Guess what, it's now a frequentist model!
01:00 Why did you look at the coin half-way through asking the question?
The act of looking might change the results for some of the audience; so do they answer before you looked, or after you looked? The Bayesian probability of course changes for you; but to some extent changes for the audience, as they've see your reaction and thus received non-zero information about the true state of the coin.
1:00 I thought it was a trick question and you were going to show the coin stading up, stuck between your fingers, to make a point about how there might not be a probability. Guess that makes me a Bayesian.
The Bayesian perspective reminds me very much of Schrödinger's cat experiment. :-)
Is it possible to be a frequentist before the coin is flipped, like the answer of that coin landing heads or tails is already 100% or 0% which is predetermined by a multitude of factors such as its orientation at the moment, how hard you will flip it and so on, all of which are all also pre-determined but we just don’t know them
How does this apply to quantum superposition?
I recommend reading the short paper Bayesian Estimation Supersedes the t Test.
Thanks for summarizing this important topic. I've no emotional investment in the Frequentist vs Bayesian debate (I've used both often in my research), but I couldn't help but feel the Bayesian perspective was not given fair credit here. The Bayesian's "point of view" should not be entirely subjective, but rather based on logical principles, that can often be derived from the laws of nature (eg. The shape and symmetry of the coin make it equiprobable to land on heads or tails). The powerful advantage of leveraging prior information for forecasting or evaluating hypotheses also ought to be emphasized more. Ideally, aspects of both Bayes theorem and frequencies should be used (eg. using base rates as prior information in diagnostics). But because the frequentist approach is so much more intuitive to use in science, the Bayesian approach is underutilized. This has been less than optimal for science which has been far too dogmatic about p-values instead. It would be nice if you could emphasize this more in future communications on this topic, thanks!
If the coin is heads-up before tossing, it will always land heads-up, and vice-versa, IF it's landing on the palm of the person tossing the coin. If it's landing on hard surface, it can go anywhere due to the bounce / twist / turn of the coin multiple times before it comes to rest. So, which one am I?
Forgive my stupid question (which might be slightly off-topic), but doesn't it matter which side is facing up before the flip, how the coin is placed on the thumb, how much force it used for the flip, and some other factors (which may or may not be negligible)?
And the Micheal Baysians don’t care I’d it’s heads or tails, as long as the camera orbits it.
And as long as there are pyrotechnics and explosions.
Great video! What are you recovering from as a statistician?
Thank you. Perfect pausing during the presentation. It is so rare among UA-cam presenters.
I'm backing the superposition, where the superposition changes based on the likelihood that you were lying in the reveal, since the coin was too out of focus to tell what the result was.
I can't believe that we are the only two people who have figured this out.
But when we talk about Bayesians view, then one would need to mention Bayesian networks. And those shall rather be compared with the coin example. Because in Bayesian Nets you would actually construct a graph with a node saying "coin was flipped" and then dealing with the probability of the coin being flipped. That's were also the strengths of a BN approach lie. When you would need to narrow down in a (short) amount of events that certainly influence the outcome. So each approach heavly relies on the hypothesis to test. The more unknown factors you have the more you tend towards a frequentists view. Right?
why is this a debate? if you have to make decisions with limited info, ie not knowing the data set (such as not having any more information prior to or after the coin flip) then you have to be Bayesian. If you know the data set, or if you're answering a silly question like "whats the probability that the coin has landed on the side that it has landed, no matter which one" then you have to be frequentist. If you wanna be technical, then frequentists have to be frequentists about all possibilities for every event, since given determinism all the coins HAVE in a sense, landed. But that's not useful from our perspective, so a lot of the time they have to be bayesian. I just don't see the debate, bayesianism and frequentism answer different questions, and which question is right to ask depends on the circumstance
Hands down the best video I’ve watched on the philosophy behind both the Bayesian and Frequentist approach. Well done
The Baeysian recognizes that the probability is relative to perspective which means recognizing the context of other's perspevtive. Perspective must involve uncertainty. The problem is that it usually loses that component. I think some people combine the two to eliminate their feeling of discomfort.
Holy crap, statistics has a place for me. Never heard of Bayesian before. I gotta do some reading now. Thank you! Seriously, that makes so much sense in my world.
Now I'm even more confused. Before the coin toss I thought that the probability of the coin landing head up was 50%. After the coin landed, it was now my chance to guess its landing side correctly to become 50% (since its landing side was already decided). Sooo, am I a frequentist?
If you are a frequentist, when the coin is landed, you will say it is either 0% or 100% (no longer a probability). But, if you are still thinking of your probability becomes 50% higher to be correct, meaning that you still think of a 'point of view' and a probability, in my opinion, this means (correct me if I'm wrong) that you think in a bayesian perspective
What if I said both Bayesian and Frequentist response and can’t decide which one :(
I first answered 50%, then thought about it while she was peeking at the coin and said: 100%. Then thought about it a bit more and said: Meh, I have no idea. What does that make me?
Then you are an Bayesian.
Why?
A Frequenists would have answered "Frequenists" and then measure how often they were wrong.
You want to guess right and therefore say both (just like a Bayesian does with the coin)
Thank You.. You are a seriously great teacher, I'd like to see your videos as a necessary part of every high school students curriculum. You remove the jargon and re-frame the learning references to simple, understandable examples which makes the learning of complex issues so much easier.
How is it possible that I only found this channel now? This stuff is brain-food-candy for any statistician like me! Keep it up :)
please explain:
so, from a bayesian perspective, yes the coin has already landed, but the core of the question is what was the probability of it having landed on heads or tails? it can only ever be one of two twings, yes or no, blue or red, up or down, always 50% to be or not to be.
I think it all depends on which hand you catch it in and which hand is over the coin and which hand is under.
what is the 'validity' of the question about probability of heads or tail once it is landed in your palm in this example is not clear ? what are its implications ?
What are the applications in real world ? Areas where they help
This is why I’ll never understand statistics beyond mean and standard deviation.
The way I thought of it was that the chance that an event did/can/will happen is actually always either 100% or 0% and it is just a lack of knowledge that makes it appear otherwise. Or in other words, probability is like a measurement of our own ignorance (are we slightly unsure or very unsure? etc). I don't know if that shit's true, it just looks like it to me.
Well said! (That's how I see it too.)
it occurs to me that most situations where you want to know a probability are Frequentist, i.e. they concern things that are already facts, but unknown to us. From a certain perspective *all* probabilities are Frequentist, if you accept that we live in a deterministic universe. All future tosses of the coin are already predetermined!
Love this post!
Cassie, thank you for detailed explanation. Please, please, please tell us more about pros and cons of Bayesian vs Frequentist approaches in the business context.
If I thought it couldn't be 50% on this instance because of the unequal forces applied to the coin. What does that make me?
This video, besides sprouting an interest in the philosophy of probability (to put it lightly) and how English sounds to those who don't speak it.
3:11 "What is the probability this coin is up heads?" Still 50%, there is apparently a third category I am part of. Or more likely the perceived dichotomy isn't one.
50% that it landed heads, or 50% that you'll guess right?
From what I've been reading in the comments, that pair of questions works better.
So, if I was to try and put that in terms I’ve spent some time with, I’d say:
A Bayesian attempt at ‘finding truth in uncertainty’/‘making predictions’ finds base rates relevant. So we cultivate relevance around the coin only landing on heads or tails, but do not place relevance on the physics of the coins’ trajectory and inertia, physical determinence, interaction with air molecules, etc etc. We use base rates as an end, and not a means to an end.
A Frequentist will cultivate relevance of those latter things, as they claim we shall assert we live in a determined universe, but in so far as we cannot fully gasp all the elements of that determination, we can use statistical models instead and judge their efficacy from the outcomes.
Is that right?
Is there a way to empirically prove there is a physical universe beyond perception?
“The truth has already been fixed in the universe”.
Powerful, powerful stuff. 🙏
And what are the odds that both the Bayesian and Frequentist throughput are calculated simultaneously by a given individual?
Hm, I'm wondering whether I can say this?:
1) Frequentist statistic is an inductive approach - trying to infer properties of the population from collected data (which also includes evaluating the assumptions of properties of the population by analysing the likelihoods of data given these assumptions --> see significance testing).
2) Probability is deductive - "knowing" properties of the population and inferring properties (probabilities) of data points from that. (And Bayes specifically includes Beliefs, which can be updated).
P.S. I'm not sure how to handle the concepts probability and Bayes - are they the same or is Bayes a special case of probability or ...?
What's the frequentist perspective on getting the model right? It always seemed to be like bayseans try to make that more explicit but I struggle to see a real distinction, but I'm kind of convinced (after adjusting my prior ;-) I just don't understand the semantic distinction that the frequentist perspective had with respect to (implicit) assumptions
I am binge watching your videos. Wish I’ve known you and your work before.
Thank you for the simple explanation :) As far as I understand, the frequentist statistics is correct. However, from my point of view as a research scientist, the frequentist statistics is often irrelevant! Because I am often interested to know if my model or explanation of a complicated reality is consistent with the observations. These types of questions are consistently addressed within the framework of Bayesian statistics. On the other hand, the Bayesian approach is still missing an important ingredient. Bayesians still do not agree on how to construct priors! How does one construct a prior, which represents one's knowledge?
If you have no prior knowledge, this can be represented as a uniform distribution over all possibilities
So would you say frequentists go with the flow?
As a kid, I used to wonder what the space between the stove and the pot was called. As an adult, I had the same issue with frequentism, I just didn't know how to formulate the question.
For that example I got Bayes. From my perspective, the coin is in an eternal state of 50/50. Until it is observed. Like quantum physics, What matters is the observation. Until I can see it, the coin is 50/50. I would say: it is just as likely to be heads up before or after the throw.
What if you make an x-ray and can see through the hand that it`s heads? Is the probability still 50/50 before you raise your hand and "see it" youth your own eyes?
@@thebrutaltooth1506 Assuming the x-ray is working correctly and it could show me that. *Yes* Because I observed it. In my opinion, an observation is any kind of measurement or reception of information through any way possible. e.g. tests, touch, etc. Evolutionary theory is based on this. We don't directly observe any of that information.
@@Lucas747G Interesting, I can respect that. Don`t know what you mean about the evolutionary theory though. You can directly observe evolution but by looking at the canges in a population not of an individual.
"The English moth, Biston betularia, is a frequently cited example of observed evolution. In this moth there are two color morphs, light and dark (typica and carbonaria). H. Kettlewell found that dark moths constituted less than 2% of the population prior to 1848. Then, the frequency of the dark morph began to increase. By 1898, the 95% of the moths in Manchester and other highly industrialized areas were of the dark type, their frequency was less in rural areas. The moth population changed from mostly light colored moths to mostly dark colored moths. The moths' color was primarily determined by a single gene. So, the change in frequency of dark colored moths represented a change in the gene pool. This change was, by definition, evolution." (Source:abyss.uoregon.edu/~js/21st_century_science/lectures/lec09.html)
So what to use in a/b testing?
Frequentist: "What is the probability the actual current state of the coin is ..."?
Bayesian: "What is the probability my estimate of the state of the coin is ..."?
It seems Frequentists try to take an objective point of view. Meaning: from the perspective of the focal object. Whereas the Bayesians take a subjective view. Meaning: from the perspective of the subject/observer.
I like that description more than her use of the word "opinion".
The explanation of frequentist thinking in the video sits uneasily with me. The idea that a flipped, but hidden, coin would be either 0% or 100% (but unknown) while an unflipped coin would be 50%, or a coin flipped and waiting to land would be 50% seems arbitrary. It's more subjective than the Bayesian explanation in a way! There are a number of reasons why the outcome might be obscured to us, whether that data is temporally obscured (you have't flipped it yet, and we experience time in one direction!), or physically obscured (a hand is in the way), or obscured through laziness (the flipped coin is in the air waiting to land and we could measure the rotation and velocity and calculate how it will spin and drop and land, but we don't bother). I don't see, on an ideological level, why it should make a difference which of these it is. So if the hidden coin is "either 0% or 100% but I don't know which" to a frequentist, why not the future event coin too?
It seems that there is something getting lost in the difference between the questions: "What side *will* this coin land?" and "What side *did* this coin land?" The frequentist as described here doesn't ever change their answer to the first question once the coin has flipped, they just start answering a different question instead, right? As I far off the mark if I were to think that maybe a change in information is being acknowledged in one case explicitly by changing the answer and in the other case implicitly by changing the question?
@@zak3744 You are correct in many things you say. In a deterministic view, everything is already determined. So, to a Frequentist this would have to mean that all coins being flipped, either in the future or past, all are determined ... and thus none have a probability. Only abstracted coins have probabilities in this sense.
Elsewhere here, I commented about this being really a linguistic difference. The difference is not really about the understanding of reality, but what question is asked.
Usually in science the Frequentist question tends to make most sense. It is about the object / objective reality. When you look at it from a decision making agent, it makes sense to look at it from a Bayesian perspective. The question is then about: what is my best estimate based on what I know? Or: the best decision based on the information available to the Agent (e.g., a robot).
I love how you explained the 2 perspectives.
So, is there a problem in statistical analysis where a Bayesian and a Frequentist would come up with different, empirically distinguishable answers? And if so, which answer would turn out to be correct?
It's important to note that frequentist theory is an incomplete theory. Bayesian inference is a theory that represents reality better -- with more accuracy. It addresses uncertainty, for any state of knowledge.
It's also important to note that frequentists try to estimate a parameter (point/range estimate) for something.
Bayesians try to evaluate degrees of plausibilities among hypotheses for a specific parameter.
These are two different approaches to the problem of trying to figure out what the parameter is. Therefore the interpretations of them are also different!
If the frequentist has a predisposed action that they like to take in a situation, does that not equal to their belief, which in turn means they are using their previous belief to take an action and update their beliefs making it Bayesian?
The problem with this test is that it has no implication. The person on the other side of the table forms opinion but does he act differently? With your coin-tossing example if there are one Baysian and one Frequentist on the other side of the table and they want to engage with you in a game of chance are they going to bet differently on a coin that you have already tossed?
A better example would be for you to toss a coin once and show the income to One Baysian and One Frequentis. The outcome is Head. Then you ask them to bet on the next income to be Head. What odds the Baysian and Frequentis would agree to?
This is a finely done video - props to Kozyrkov for a superb presentation.
I think, however, the emphasis on the subjectivity of Bayesian inference is a bit misleading. One comes away with the notion that frequentists are interested in reality while Bayesians are interested in opinions. Surely all practitioners of data-based inference are interested in reality; the difference lies in kinds of questions by which reality is sussed out.
The Bayesian and the frequentist might agree that a given state or process in the world can be understood in terms of definite parameters, i.e. that the flipped coin has already landed. To say that the Bayesian approach is subjective is simply to say that it is concerned with *our knowledge* - or, equivalently, our *uncertainty* - regarding the parameters of interest given available evidence (data + priors). I suppose this could be called "subjective" since it depends on the knowledge available to a subject, but it is certainly not subjective in the pejorative sense of "arbitrary."
In most cases, at least in my field of ecology, the frequentist is also interested in parameter states. That, after all, is what it means when we ask whether X causes Y. But frequentist methods get there indirectly by inferring the likelihood of evidence (data only, no priors) given assumed parameter states. While these approaches generate parameter estimates (parameter values that maximize the likellihood of the data) with uncertainty (intervals that would contain the true parameter value in X% of hypothetical repetitions of the sampling and analysis process), they do not tell us directly what we really want to know: what should we believe about the unknown state of the paramater? This is what we want to *know* because it guides what we want to *do*, i.e. to understand and potentially intervene in the world. These objectives, like our knowledge, are intrinsically subjective, but in a sense that is both legitimate and unavoidable.
I also think it is a mistake - not one made explicitly by Kozyrkov, but one occasionally suggested by others - to project approaches to data-based inference onto metaphysics. Choosing between frequentist and Bayesian methodologies should have nothing to do with whether one is an ontological realist or nominalist. As Andrew Gelman puts it, "theoretical statistics is the theory of applies statistics." Pragmatic handling of uncertainty, appropriate to the question at hand, is the only end for which statistics is a legitimate means.
Take the coin flip as done and in her hand unseen. Now suppose you have to make a decision which will result in your death if you get it wrong (or some equally bad out come). Which approach will give you the most reasonable model ?
I sense a little bias on this video. What is the probability that it's towards frequentist?
just came across this wonderful video, very simple explanation, read many articles but still confuse with the technical terminologies they have used in the paper. from this video within 5 minutes i have understood the concept. Thankyou Cassie for sharing wonderful knowledge with us. really appreciate it :)
Why the vid says at the beginning, "for philosophical reasons, pretend you're watching this live"?
I kind of understand, a frequentist sounds like they care about what is "possible", if there are two possible options, like heads or tails and an event which has a before and an after.
Before the event we can consider those 2 possibilities.
After the event we can consider the outcome but there is no possibilities to consider, as one them was realised.
If you have been taking prior beliefs and outcomes into account then you would have something to consider.
Really makes me think of the Monty Hall problem, because that hinges on the fact that Monty Hall has more information than you do -- just like Cassie looking at the coin while we don't see it. Is the conclusion that you should switch doors in the Monty Hall problem based on Bayesian or Frequentist analysis? Or is there a case to be made using either?
As I recall, a simple truth table should do it. There's simply more positive outcomes from switching than not.
Neither, because it's not a statistical problem, but purely about probability theory.
For me, Bayesian. With Bayesian, your own knowledge affects the probabilities you calculate for yourself. You can add information to your calculation and adjust your personal estimates. With standard Monty hall, you pick a door and calculate 33% chance of winning. Monty opens one door and the one that was neither opened nor chosen now has a 66% chance of being the winner. The one you chose still only has a 33% chance of being the winner, so switch.
But now the twist. Imagine, at this point, a second contestant walks in and is also given the choice of one of the two doors. They see the exact thing you do, two closed doors and one open. But being late to the party, they will only have a 50% chance of picking the winning door compared to your 66%. Bayesian can easily handle this.
Can a frequentist view reflect these simultaneous yet differing odds. Maybe someone could show us how a frequentist would handle this shift in odds based upon personal knowledge?
You seem to be assuming that each one is not useful in different circumstances both are useful depending on what is knowable and what you plan on doing next.
Hey is that a Sri Lankan Yaka mask in the background?
what if someone told you that your interaction with the coin make it certain and as long as your hand is still on the coin the probability is 1/2?
Finally I get the point of difference between them but I am more confused now which of these I am ? How to deal with that ?
I don't know anything about statistics, but it sounds like when each group answers the "what probability is it that it's x?" question, they're focused on two different referents. The frequentists interpret the question as referring to the actual, determinate state of affairs in the world, while the Bayseians interpret it as an epistemological question, that is as a question about our knowledge. Two ways of interpreting what "probability" refers to.
Can you do a video on the confidence density vs the posterior density?
I saw a different video on confidence vs credible intervals. This was my comment: The long run performance of the 'ensemble' of intervals is what gives us confidence the observed interval indeed covers the true value. We can therefore say we are 95% confident the observed interval indeed covers the true parameter. It is nonsensical to consider the population level parameter as an unrealized or unobservable realization of a random variable that depends on the observed data just so we can make philosophical probability statements about the parameter. Unless the parameter was sampled with replacement from the prior distribution and a new value sampled from the posterior, it is absurd to attribute posterior probability statements to the parameter. While the p-value is typically not interpreted in the same manner, it does show us the plausibility of a hypothesis given the data. It is the inversion of a hypothesis test that gives rise to the confidence interval. See confidence distributions, confidence curves, and confidence densities.
I am thinking about how this would apply to political polling and election simulations. I'm not sure how i would use this information to help me there...
From what I know, vote polling usually uses a Frequentist approach (notice that they almost always have a margin of error attached, which is a concept from the frequentist framework).
Thanks for the video! Nice way of explanation
To frequentist, what is the mechanism of randomness then?
Clear explanation, thanks. Will it be possible to have a mathematical explanation as well, such as doing the same analysis (for instance comparing mean across two groups) using Frequentist (a t-test) versus Bayesian approach (?) ?
What a beautiful philosophical view statistic perspective. Loved it!
I think I miss somewhere the point. Is the question about the occurence of a thing under uncertainty? But then I understand the Bayesian as a theory about all occurences [because (s)he starts already with a theory] (of a certain kind of thing) under uncertainty. So (s)he would say: in the end, if you look at the data and your hypotheses then there is a 50% probability that either head or tail. But the frequentiast would look only for this single occurence. This single occurence can only have one truth value either head or tail. So either his/her guess is wrong or right. But in the end, if the frequentist would make enough coin tosses (s)he would likely progressingly (?) to come to the hypothese that from all coin tosses, half of them is head, half of them is tail. So they would share the same opinion about the distribution of heads or tails.
Bayesian. The point is you dont know so it is 50%
Its guessing.
The frequency approach is useless.
And at least Bayesian willing to admit its' own bias. Frequentist on the other hand makes assumption without consideration. As a result, Bayesian helps the field of ML alot and Frequentist doesn't.
Let's remember that a mathematical model isn't inherently right or wrong, it's useful or not.
And yes, the frequentist model is mostly useless.
Pretty bold to consider a whole area to be useless. All models have limitations and like anything other thing, when frequentist statistics is done correctly, it can be useful
You know nothing about statistics, and you know less about mathematics.
I love this.. However, you ask the question, what is the probability the coin is heads up on my palm? My answer is 100%, as you have both palms touching the coin, therefore it is 100% probability the coin is heads up and tails up on your palm. Does that thought process make me a Bayesian or Frequentist?
Technically correct is the best kind of correct.
Tautologically correct is a kind of correct.
🙃
Are the chances of “guessing” coin flip correctly for frequentist 100% then? am I missing something here?
I am kinda confused as well... The implication of a question like that tends to be "What is the probability [that you could correctly guess] that this coin is heads-up on my palm?" Because, in a situation where you aren't taking everything as directly stated, like a casual conversation, I would say, and I would assume most would say, "It's 50%." But if the question was asked more directly, making sure to directly state that she is asking the probability of the coin's state itself and not your guess of it, then I believe that most would have a Frequentist response.
PsiGreen Thats perfectly right, BUT only when you don’t care about the outcome. See, If you know its a Head, then you wont be using probability. If you are to guess we arrive at 0.5. If you don’t wanna look or guess then why do the whole bloody experiment? Its a moot point really.
Can someone give me a nontrivial example of a good frequentist approach as we almost never actually know the probability of an outcome or are blindsided by an outcome we never even anticipated.
With clearly defined axioms/system, Bayesians are the objective ones and frequentists are the subjective ones, being led by statistics of a data sample. Am I claiming this opinion of mine is true because I am a Bayesian?
Would being a Bayesian or a frequentist affect how one might respond to the sleeping beauty problem?
What does any of this have to do with the choice of doors in the game show, Let's Make a Deal?
I'm trying to do Bayesian inference where the prior and likelihood distributions are Cauchy distributions. Can you (or anyone else) point me in the direction of how to do that? There are lots of resources online of how to do Bayesian inference with normal distributions and beta and gamma distributions, but I don't see anything involving Cauchy distributions.
Loved this!
You're a damn good teacher madame! If you are not using that talent somewhere along your path, then it's a crying shame!
Who are you @cassie Frequentist or Bayesian
Wow. Accidentally I came across this video and it has rattled my thinking. What type one is when their beliefs are shattered.
A smart type. Means you are open to fixing biases
I am not sure I really got the difference (I know nothing about the subject):
"The frequentist will say there is a 0% or 100% chance, but I don't know the answer." Fine, but there is a 50% chance of your guessing it correctly. Therefore, the Bayesian is simply skipping a step and merging the 50% chance of guessing correctly with the chance of the coin falling heads or tails.
So, in reality:
a) before you toss the coin, (i) there is a 50% chance of being heads or tails; (ii) you have a 50% chance of guessing if it is heads or tails;
b) once the coin has landed and you can't see it yet, you still have a 50% chance of guessing it correctly;
c) scenario (b) is the exact same as if you guessed before the coin was tossed and nobody hid the result (like in sports matches when they fall to the field/court).
Your guessing chances don't change on whether the event has already happened. If the result is not revealed, you still have a 50% guessing chance no matter what. Because your guessing doesn't influence the result, both perspectives are reaching the correct answer, but only highlighting different parts of it.
Maybe I am taking the example to literally, but it does not sound to me like two conflicting viewpoints.
"opinion" vs "no opinion" ! But what about the "opinion"/metric on what the Frequentist's methods quality is aka "what is the lower threshold of 'good enough' " ?
It's curious to think about probability and statistics theories in physics. In my perspective, the experimental physicists generally goes with a Frequentist mind, since the common mindset is to try the same experiment over and over and look what percentage they got a "good answer". In the other hand , the theorists care too much about perspective and information, actually the quantum theory is bounded to theses concepts, hence, the resolutions of the problems are made from a Bayesian mind. Your videos are awesome! Loved it!
Statistical probability is a measure of ignorance, not certainty. Everything that Does happen always had a 100% chance of happening, we just didn't have enough information to know it. The two perspectives are perfectly compatible.
Also, knowledge is justified belief.
Agree on the first bit, but not on the second. Knowledge is not simply justified belief, some does occur that way but much is also direct knowledge that does not require a belief.
There is no such thing as rigid distinction between the two, I use both, just not for the same reasons obviously. Why would you choose only one anyway? There isn't a better one, so don't choose, both are important, and both can be very useful to consider in a same situation to see different things, it helps resolve problems in (unusual sometimes but) effective ways.
I'm just gonna leave it here but if rings any bell to somebody: I try to never be content with my deductions or ways of seeing and conceiving things, so I try to force myself to see from perspectives where I'm always wrong, even if it's from stupid reasoning/perspectives, it helps see unexpected things and patterns sometimes where we expect them the least and it drastically help understanding notions of relativity.