I discovered this channel in youtube search and guess what it burnt all my frustration and I love the way to make people understand topic in this video!
Great video, thank you. I was often confused between probability and likelihood and would just move on to the next topic still not fully understanding the difference, the "multiple universes" idea is the key part for me which finally explains it! Thank you.
The clarity you provide--as in, what the zero or 1 on the x-axis of the normal distribution represent but more importantly what they don't represent, which has been a source of confusion (and a drag) for me, is now more clear and finally validates a hunch/H-sub-A I've held; too many terms in statistics which I've encountered have been near-tautologies and a gigantic obstacle for me. In my humble and quasi-researched opinion about learning, cognitive transfer, linguistics, and abstraction, I postulate that for a new subject, especially those often found as hardly intuitive (clearly as a function of many factors), require the most clarity and for me an exhaustive list of features and areas of overlap, as well as an explicit articulation of the areas or features an idea does not connect with. THANK YOU for the excellent presentation!
An Amazing video and explanation. All these other videos only said points on the probability density function are likelihood but it didn't make any sense to me. the way you explained it cleared everything.
Great video! I'm just curious: When you say "we don't know which universe we're in," is this just another way of saying, "we don't know the probability distribution of the coin"?
Amazing, if i got correctly its like In probability, we start with the whole and then delve into the details, but in likelyhood, we begin with the details and then move to the whole.
Yup, in probability we start with the situation/universe/parameter and find the probability of outcomes. With likelihood, we start with the outcomes and try to figure out the situation/universe/parameters!
05:30 The probabiliy that X=1 is 1. It's certain since we've already observed it. The question makes no sense simply because it makes no sense to talk about probability for something that already happened. The same holds true even for discrete probability.
The implication is that our observation X=1 is just one *sample* from a probability distribution of a random variable X that has a distribution, and other samples will not all be X=1. So the P(X=1) is not one, but P(this particular realization of X is 1)=1, yes.
@@statswithbrianI see. You meant to ask what is the probability that the next observation will be one given that we have already one observation with X=1.
At 5:06, in the yellow box said "It is NOT a likelihood in this context either" confused me. When dealing with a single data point, the likelihood function is simply the probability density function (PDF) evaluated at that point. So, the likelihood of observing a specific value x from a normal distribution with mean μ and variance σ² is given by: L(μ, σ² | x) = f(x; μ, σ²) where f(x; μ, σ²) is the PDF of the normal distribution. Therefore, for a single value, the likelihood and density value are equivalent.
Yes, they are the same number, but the interpretation is different. A likelihood might be the same number as a pmf or pdf, of course, that’s the entire point of the video.
@@ecarg007You seem to understand that likelihood is sometimes the same number as a pdf. But a likelihood and a pdf are never going to have the same interpretation because a likelihood is not a probability. Not sure what you’re trying to say about statquest’s video.
@@statswithbrian"It is NOT a likelihood in this context either", here "in this context" does it mean the following? In the density function with x=1, the density value is 0.2419707, it is not a likelihood. But you can say, the likelihood of observing x=1 from a normal distribution with mean 0 and variance 1 is 0.2419707.
@@ecarg007 when we know the true parameters are mu = 0 and sigma = 1, 0.2419707 is the probability density at x=1, which allows us to compute probabilities around x=1. When we do not know the true parameters and only know our observed data x=1, 0.2419707 is only the likelihood in the universe where mu = 0 and sigma=1. The likelihood would be a completely different with different parameters. For example, when x = 1, the likelihood is 0.3989 when mu =1 and sigma = 1. So 0.3989 and 0.2419707 cannot both be probabilities (or probability) densities in this context. They are likelihoods under different scenarios.
@@999shastathis case will be added in the universe and the probabilities will still add up to one. It's a null-sum game. Not like with likelihood where if we add another case (a new model or another possible source universe if we're comparing universes instead of models/distributions), its likelihood will be calculated the same way and it'll get its own value. Nothing happens to the other values that stay the same. With probability, the other values need to change to make room for the new one.
@@statswithbrianlikelihood is not about the outcome. It's about the process/model/distribution that hypothetically produced the already observed outcomes. It's just a number, calculated the same way and used to rank or compare candidate processes/models/universes. We don't really care about the order of magnitude of the numbers obtained. Just their relative order.
Sure we can rephrase and talk about the likelihood of the outcome under a given candidate model. But this is the best way to confuse people and that's why many stiĺl struggle with the concept. It's just that the way chosen to calculate the likelihood is to take a candidate model as given then to find the corresponding value of its pdf for the observed outcome. If there are many outcomes, we just multiply their pdf values. This alone show that we don't really care about the exact value of the likelihood since it depends the number of observations at hand.
7 місяців тому+1
Incredible explanation, clearest I found out there, 🎉
Lately I've been introducing LRT, or tests in general, to my coworkers like "I would bet you with 1:20 odds that this coin is rigged, would you take this bet?"
A Very nice explanation. We poor experimental physicists (and any other scientists whose discipline is base on observations) deal almost exclusively with likelihoods - we use observations to draw conclusions about the (a priori unknown) properties on the actual universe. Theoretical physicists, OTOH, postulate those properties and calculate probabilities of what we _should_ observe. Then we compare the two.
No worries, Martin - you only really need to know what "likelihood" is if you're doing advanced statistics stuff anyways. In everyday language, these words mean the same thing, and even in statistics, they are really not so different!
Why does this reminds me of StatQuest?
We both use Keynote to make the slides :)
I was thinking the sameee 😂
loving it too ❤
The contents are not the same, both are useful. Thank you.
Universe!!! It had broken my stone, my head. Thank you!
I discovered this channel in youtube search and guess what it burnt all my frustration and I love the way to make people understand topic in this video!
Great straightforward intuitive explanation.
Seriously very clean and simple explanation , keep continuing these lectures
finally find a easy understood explanation, thanks Brian
Great video, thank you. I was often confused between probability and likelihood and would just move on to the next topic still not fully understanding the difference, the "multiple universes" idea is the key part for me which finally explains it! Thank you.
Great video! That part with the normal distribution at the end and juxtaposing x and mu as the different unknowns was super helpful.
I’ve had 7 statistics courses at the graduate level, and no one has ever explained what likelihood is.
Thank you.
The clarity you provide--as in, what the zero or 1 on the x-axis of the normal distribution represent but more importantly what they don't represent, which has been a source of confusion (and a drag) for me, is now more clear and finally validates a hunch/H-sub-A I've held; too many terms in statistics which I've encountered have been near-tautologies and a gigantic obstacle for me. In my humble and quasi-researched opinion about learning, cognitive transfer, linguistics, and abstraction, I postulate that for a new subject, especially those often found as hardly intuitive (clearly as a function of many factors), require the most clarity and for me an exhaustive list of features and areas of overlap, as well as an explicit articulation of the areas or features an idea does not connect with. THANK YOU for the excellent presentation!
Thank you, absolutely!
Clearly explained the complex concept.
Amazing. Enlightening
Excellent!
An Amazing video and explanation. All these other videos only said points on the probability density function are likelihood but it didn't make any sense to me. the way you explained it cleared everything.
Thank you! So glad you found it helpful!
By God what an absolutely amazing video.
Great video! I'm just curious: When you say "we don't know which universe we're in," is this just another way of saying, "we don't know the probability distribution of the coin"?
Yes, exactly!
Amazing, if i got correctly its like In probability, we start with the whole and then delve into the details, but in likelyhood, we begin with the details and then move to the whole.
Yup, in probability we start with the situation/universe/parameter and find the probability of outcomes. With likelihood, we start with the outcomes and try to figure out the situation/universe/parameters!
Great explanation! Naver really what is the difference between these two.
Best explanation 👌
noice...the graphics helped a lot
05:30 The probabiliy that X=1 is 1. It's certain since we've already observed it. The question makes no sense simply because it makes no sense to talk about probability for something that already happened. The same holds true even for discrete probability.
The implication is that our observation X=1 is just one *sample* from a probability distribution of a random variable X that has a distribution, and other samples will not all be X=1. So the P(X=1) is not one, but P(this particular realization of X is 1)=1, yes.
@@statswithbrianI see. You meant to ask what is the probability that the next observation will be one given that we have already one observation with X=1.
@lbognini I definitely did not mean that. That is a Bayesian concept (a posterior predictive distribution) that is not related to this.
At 5:06, in the yellow box said "It is NOT a likelihood in this context either" confused me.
When dealing with a single data point, the likelihood function is simply the probability density function (PDF) evaluated at that point. So, the likelihood of observing a specific value x from a normal distribution with mean μ and variance σ² is given by:
L(μ, σ² | x) = f(x; μ, σ²)
where f(x; μ, σ²) is the PDF of the normal distribution.
Therefore, for a single value, the likelihood and density value are equivalent.
Yes, they are the same number, but the interpretation is different. A likelihood might be the same number as a pmf or pdf, of course, that’s the entire point of the video.
By the way, with quite different explanations at 3:33 of ua-cam.com/video/pYxNSUDSFH4/v-deo.htmlsi=vI0gQGTKWks68Hhm
@@ecarg007You seem to understand that likelihood is sometimes the same number as a pdf. But a likelihood and a pdf are never going to have the same interpretation because a likelihood is not a probability. Not sure what you’re trying to say about statquest’s video.
@@statswithbrian"It is NOT a likelihood in this context either", here "in this context" does it mean the following?
In the density function with x=1, the density value is 0.2419707, it is not a likelihood. But you can say, the likelihood of observing x=1 from a normal distribution with mean 0 and variance 1 is 0.2419707.
@@ecarg007 when we know the true parameters are mu = 0 and sigma = 1, 0.2419707 is the probability density at x=1, which allows us to compute probabilities around x=1. When we do not know the true parameters and only know our observed data x=1, 0.2419707 is only the likelihood in the universe where mu = 0 and sigma=1. The likelihood would be a completely different with different parameters.
For example, when x = 1, the likelihood is 0.3989 when mu =1 and sigma = 1. So 0.3989 and 0.2419707 cannot both be probabilities (or probability) densities in this context. They are likelihoods under different scenarios.
thank you!
Love your videos!!!
Recommend me good books in mathematical stats, please!
Thank you! My personal favorite is the classic Casella & Berger!
The single word 'universe' made it all clear! Thank you for a neat perspective :)
As they had no wings the strangers could not fly away, and if they jumped down from such a height they would surely be killed.
Great video
Even if the coin is not fair the probabilities still adds up to one.
That is very true! Likelihoods of a single outcome under multiple probability distributions, however, do not add up to one.
Unless it lands on it side
@@999shastathis case will be added in the universe and the probabilities will still add up to one. It's a null-sum game. Not like with likelihood where if we add another case (a new model or another possible source universe if we're comparing universes instead of models/distributions), its likelihood will be calculated the same way and it'll get its own value. Nothing happens to the other values that stay the same.
With probability, the other values need to change to make room for the new one.
@@statswithbrianlikelihood is not about the outcome. It's about the process/model/distribution that hypothetically produced the already observed outcomes.
It's just a number, calculated the same way and used to rank or compare candidate processes/models/universes.
We don't really care about the order of magnitude of the numbers obtained. Just their relative order.
Sure we can rephrase and talk about the likelihood of the outcome under a given candidate model. But this is the best way to confuse people and that's why many stiĺl struggle with the concept.
It's just that the way chosen to calculate the likelihood is to take a candidate model as given then to find the corresponding value of its pdf for the observed outcome. If there are many outcomes, we just multiply their pdf values.
This alone show that we don't really care about the exact value of the likelihood since it depends the number of observations at hand.
Incredible explanation, clearest I found out there, 🎉
Thank you, glad you liked it!
Can you do coupling some time? I know it's important to the earth mover problem.
I don't know much about it, sorry!
@@statswithbrian Ok me neither :)
Thanks
Define "Fair coin" there is only two sides in a coin, are there universes where coins have 3 or more sides?
No, a fair coin is a coin where heads and tails are equally likely.
Lately I've been introducing LRT, or tests in general, to my coworkers like "I would bet you with 1:20 odds that this coin is rigged, would you take this bet?"
"No sir, I don't gamble. (alpha = 0)"
A Very nice explanation. We poor experimental physicists (and any other scientists whose discipline is base on observations) deal almost exclusively with likelihoods - we use observations to draw conclusions about the (a priori unknown) properties on the actual universe. Theoretical physicists, OTOH, postulate those properties and calculate probabilities of what we _should_ observe. Then we compare the two.
The best explanation on Likelihood ever!!
Thanks Terry!
I am glad I did not major in statistics....Still don't get it....
No worries, Martin - you only really need to know what "likelihood" is if you're doing advanced statistics stuff anyways. In everyday language, these words mean the same thing, and even in statistics, they are really not so different!
pr ( getting a head tossing a fair coin ) = 0.5 or a half
I love you.
Wish you were my prof :/
I once flipped a nickel onto the floor, near a wall. It bounced off the floor, one-hopped the wall, and landed on the EDGE of the nickel.
Such acts of God are being the tools of probability.