In Statistics, Probability is not Likelihood.

[@statquest]

In common conversation we use probability and likelihood interchangeably. However, statisticians make a clear distinction that is important to understand if you want to follow their logic. The good news is that they are both super simple. The bad news is that they are easy to get mixed up. This StatQuest gives you visual images that make them both easy to remember so you'll always keep them straight. NOTE: This video was originally made as a follow up to an overview of Maximum Likelihood kzbin.info/www/bejne/jpbTiaeibr5-rcU . That video provides context that gives this video more meaning. So if you are wondering what a likelihood of 0.21 represents, please watch that video.

[@nemlas85]

the distinct use of the word "likelihood" always assumes normal distribution?

[@statquest]

@@nemlas85 The word "likelihood" applies to any statistical distribution. In all cases, it refers to the y-axis coordinate that corresponds to a specific x-axis value.

[@MichaelJSpraggon]

Would a better word for probability be 'confidence' or 'rational confidence'? For example: the average probability of of an unbiased 6-sided die landing on a 6 is expected to converge on 1/6 over many throws, but the probability of any particular throw landing on a 6 is either 0 or 1. However, the observer doesn't know enough about the conditions of the throw (which were a series of causes and effects from the beginning of the universe leading to the inevitable result) only that the die is symmetrical with 6 sides. Therefore they can only be 1/6th confident in predicting the correct outcome.

[@BulkySplash169]

I am a postdoc in neuroscience/psychiatry on a mission to brush up my stats knowledge. I can only repeat what others have already said: It's amazing how you break down and explain complicated topics in an understandable way. Thx so much for these videos.

[@statquest]

Thanks!

[@ExistenceUniversity]

When I was doing my neuroscience undergrad, I had to help the TAs in the Stats lab courses as I was the only person that understood math lol. Even still, I wish these videos existed when I was taking the course.

[@viktor8050]

This isn't complicated topics. Anyone can learn and understand this.

[@Fahumsixtysix]

Wild that a STEM postdoc would not know the difference

[@charlesdarwin5185]

Statistica Mac version is the best self learning tool for statistics.

[@graymars1097]

After spending 2 hours on KZbin learning about probability and anything related to it, I landed on this video and I want to say this: I LOVE YOU

[@statquest]

BAM! :)

[@Arivan_Abdulla]

@@statquest Double BAM!

[@patheddles4004]

Right, so: - Probability is for predicting an outcome within a known system (eg. rolling fair dice) - Likelihood is for analysing an outcome when the system is not known for certain (eg. determining if particular dice actually are fair, or determining what curve is the best model for a dataset) I just learned a thing - thank you. :-)

[@statquest]

yep.

[@peabody3000]

ahhhhh

[@atanyhdra]

@@statquest BAM!!

[@AlexandroGarcia6492]

Damn i get it now Thanks!

[@suivzmoi]

probability is the quantity most people are familiar with which deals with predicting new data given a known model ("what is the probability of getting heads six times in a row flipping this 50:50 coin?") while likelihood deals with fitting models given some known data ("what is the likelihood that this coin is/isn't rigged given that I just flipped heads six times in a row?"). I wanted to add this perspective because using the example in this clip, a likelihood quantity such as 0.12 is not meaningful to the layman unless it is explained exactly what 0.12 means: a measure of the sample's support for the assumed model i.e. low values either mean rare data or incorrect model!

[@statquest]

That's exactly right! Thanks for posting your comment.

[@mohamedrefaat197]

Thanks for clarification

[@LuisPereira-bn8jq]

That's what I was thinking. I've taught plenty of Probability courses, and I really wasn't sure what this "Likelihood" was supposed to be conceptually. The issue being that Likelihood as described here isn't really concept, it's just a computational tool used in the intermediate steps for fitting models. In fact, if you go a step further you turn the set of possible models into a probability space itself, and then Likelihood is itself a probability again.

[@dreaminglucid1316]

Thank you for easy explanation!!! In addition.. The Probability of an event is 0... that is, 1/infinite. Therefore, We should compare the cumulative probability between events. But we can compare the y values between events. Definition of Likelihood in easy : y value of PDF. Countable Events : Likelihood = Probability. Continuous Events : Likelihood =/= Probability. Likelihood = PDF. Have a nice day!.

[@suivzmoi]

@@jamescollier3 when you say "10 percent" you are talking about probability (area under the curve). likelihood is instead just an instantaneous point on the curve. 0.12 does not equal "12 percent". it is at the moment just a number for one data point. you would compare it to another datapoint which would have its own likelihood given the assumed model, e.g. the likelihood of getting a 34g mouse is 0.15, or, it is more likely given the model that a randomly selected mouse is 34g instead of 32g. if you wanted to to quantify it in layman terms you would use probability instead. such as, given this model, 68% of the time the mouse should be 34g +/- 2.5g

[@zerosiii]

Seriously, please don't stop making these! You really nail the topics in the most perfect time, and always explain them in awesome ways :)

[@elderhiker7787]

This is good stuff. Although I have taken 3 graduate level statistics courses, I struggle to explain the rationale behind the concepts. Which means, of course, that I lack deep learning of statistics. Your straightforward and graphic explanations are marvelous; even better than my stats professors. Thanks and I’m a subscriber now.

[@statquest]

Thank you very much! :)

[@mihailyanchev1905]

While doing my PhD in Economics and ML I ran into a neat explanation of the distinction. Probability is to likelihood like theory of probability is to statistics. The first deals with the outcomes in terms of population characteristics given population parameters. The latter deals with the inverse: trying to infer the population parameters given samples of the populations. Therefore, a probability is a population parameter, while likelihood measures how likely is to have a given population parameter based on the observed data in a sample.

[@skandagurunathanr4795]

I was completely confused on the concepts, after referring lots of videos and confusing intuition I just came to this channel. The song you play at the starting of this video just refreshes the learning journey. The content you give with clear intuition makes me really very very very very very happy...

[@statquest]

Awesome! :)

[@ian-haggerty]

I think it's worth mentioning that "likelihood" is otherwise described as "probability density". We call it a "density" as it is literally the probability per unit mass (in this context). This also means that the *unit* of likelihood is the reciprocal of the unit on the horizontal axis, in this case: probability per unit gram. The choice of unit is arbitrary, and so the value of the likelihood is dependent on the unit of mass you care to choose. This also has a bearing on the numerical values for the mean and standard deviation. Josh-I love your work! Just offering up my slice for constructive feedback/food for thought / follow-up ideas.

[@statquest]

Thanks!

[@Stew282]

Wow and gosh! I work a lot in risk management and have long argued for the appropriate use of the terms 'likelihood' and 'probabiltiy'. As far as most poeple are concerned, they are synonymous. People cannot understand the difference between the likelihood of a specific event and the probability of an event causing a specified outcome. Thanks for the simplification.

[@statquest]

Glad it helped! :)

[@gurditsinghchandok1641]

came here after watching his logistic regression vids..the clearity of these topics is insane!! thanks a lot :)

[@statquest]

Glad it was helpful!

[@morganjones7428]

Yeah, the clarity of this guy's explanations are off da chartZz!!

[@sannwailhyan5113]

I studied financial econometric for past two semester, now I am at third semester, doing special project/thesis, all the concept I studies, becomes linked after I watch your video, I just want to say I really appreciated your explanations. I am pressing likes for every videos I watch going forward. Maybe after my project, I will learn machine learning. Thank you.

[@statquest]

Thank you! :)

[@sarrae100]

StatQuest , you're the best when it comes to "making it Simple"

[@statquest]

Thank you! :)

[@becauserocks.5784]

Duuuude, I've been doing data science for about 5 years now and stats for a lot longer and this is the best explanation every. I'm stealing this!

[@statquest]

Hooray! :)

[@DianNuryani-x5b]

this is the most understandable explanation out of all videos i've seen so far about the differences between probability and likelihood.. thankyou so much

[@statquest]

Glad it was helpful!

[@abdallahbahyabdelazimothma8359]

wow!! that was the most clearly explained math video i have ever seen, thank you so much

[@statquest]

Thank you! :)

[@EnlightenNook]

I was trying to understand likelihood from yesterday but unable to understand properly, this the best video which explained me in very simple way. Thanks

[@statquest]

Thank you! :)

[@mastermike890]

Your intro songs have really grown on me. You are like the Bob Ross of Statistics.

[@ionahrapsa5146]

Very well put

[@benphua]

Haha agreed!

[@nathanlewis42]

Now I’m worried that if I subscribe I’m going to loose my taste in music.

[@annapeng88]

Totally agree Bob Ross of Statistics haha

[@immanuelkant7895]

Bob Ross was a painter, not a musician...

[@missregita]

as a student who majors in statistics, all of your videos are so helpful! thank you❤

[@Hamromerochannel]

I never thought I would be saying I like stats. As you grow older, you will see the importance of stats in the real world you start to appreciate it more

[@statquest]

Bam! I think what you say is true. The older I get, the more I appreciate the variation that I see in the world around me. And the more I appreciate variation, the more I appreciate statistics as a way to understand it.

[@denizersoz7012]

This is a major issue with the current Math education. We skip teaching the most useful part. Probabilities, statistics and how to make decisions should be way more integrated in our education system.

[@MadhushreeSinha]

statquest makes feel very very very happy indeed!

[@statquest]

Hooray!!! :)

[@chiragvartak5658]

Oh man. I had thought you did these songs at the start just for the memes. But I checked out one or two songs from your discography. They're prettty good!

[@statquest]

Thanks! :)

[@plitser9880]

this is definitely one of the best 5 minutes i've ever spent in my life.

[@statquest]

bam! :)

[@sarthakdua3234]

Crisp, concise and to the point! Instantly cleared my confusion!

[@statquest]

Hooray! :)

[@tunneloflight]

A truly excellent and simple presentation of Bayes theorem and more importantly about how it can go horribly awry in practice. It is always important to remember as you so well describe that it is an estimation of probability conditioned on our state of apparent knowledge and not a statement about truth. For that we need the actual data from the world. It is all too easy to forget this and get into a recursive loop where this unintentionally instead becomes a tool to support confirmation bias.

[@statquest]

noted

[@ob96275]

Thank you for solving my questions that keeps staying on my mind for years. This helps a lot!

[@xiukuiji747]

Wish I have came across this channel earlier, subscribed after just one video. Keep up the good work man. Awesome contents and nice lil song at the beginning.

[@statquest]

Awesome, thank you!

[@JMRG2992]

I just noticed something interesting. In my native language (spanish) the word Likelihood doesn't have a special word to be defined, like Josh is saying in english where exists a difference between likelihood and probability, if one checks the translation of likelihood to spanish it would equal to "probability" so it appears on spanish the word just does not need to be differentiate but in english it is !

[@statquest]

This problem is actually the same in English. In normal conversation, "probability" and "likelihood" are equal and mean the same thing. Only in statistics do they mean different things. This is why these terms are so easily confused, even by native english speakers.

[@diegofabianledesmamotta5139]

In spanish, some professors use the word "hope" in addition to "probability." Years later, I find this video and suspect a lot happened that I didn't notice. 🤨

[@misiek_xp4886]

​@@diegofabianledesmamotta5139 In polish we used to call expected value "mathematical hope". We don't differentiate probability and likelihood too.

[@ZetaFuzzMachine]

@@diegofabianledesmamotta5139 oh boy, I'm lucky I studied Bayesian stats. in English!

[@jaijeffcom]

I really like your whole channel. You make things very clear, and you give a charming and personable presentation of it all. Thank you!

[@statquest]

Wow, thank you!

[@shenzou4778]

StatQuest makes me feel so happy... so very very very very very very very very..... Happy! StatQuest! I mean seriously, yeah!!!!!! love this channel from China!

[@statquest]

Thank you very much! :)

[@madghostek3026]

Cool thing that helped me understand this long time ago, it's related to solving maximum likelihood: We know probability sums up to 1 if we consider all the options, but likelihood not necessarily. Let's say we have a natural number P that is some kind of paremeter, it is used to build an estimator that predicts if a coin will land on head or tails, maybe it's a mathematical model. If the parameter P doesn't even contribute to the prediction, as in the prediction is dumb no matter what, any estimator will have the same likelihood. And since the P is a natural number, integrating over dP will just diverge, because the likelihood is constant... doesn't sound like probability so much now.

[@susovan97]

I do see your point, but to me likelhood is just a probability mass or probability density, that's a function of the unknown parameters of the distribution, given a sample from that distribution.

[@aishah8398]

my head was boiling coz of PCA and it's a blessing that I came across the statquest video ... thank you for making these topics so clear n interesting... stay blessed

[@statquest]

Thanks!

[@Nakameguro97]

Wow! That was the clearest, most concise explanation of likelihood that I've ever seen! Many thanks. ^^

[@statquest]

Thank you! :)

[@joshuadimick723]

"Jibber Jabber clearly explained" is t-shirt worthy!!!

[@statquest]

That's a great idea! BAM! :)

[@justtoleavecomments3755]

Actually makes things so much more intuitive, thank you!

[@statquest]

Hooray! :)

[@nikitaarora347]

Pls keep on making such videos, you might as well prevent me from feeling stupid. Thanks a tonne.

[@statquest]

Thanks! :)

[@michaelduncan5805]

Maybe this seems overly simple for some, but this was awesome! Thank you!

[@neon7874]

statquest again after so many yrs thx youtube algo gods

[@statquest]

Bam! :)

[@akhilachillara1845]

Hi Josh, I really love how you simplify statistics concepts. After watching above video, I have this question, Does likelihood always have to be a single point and not a range? Can there be a question like, What is the likelihood of weighing a mouse between 32 and 34 grams? Will the likelihood also be a range in that case? Like between 0.12 and 0.13 or something like that?

[@statquest]

That's a good question. The problem is that in normal conversation, "likelihood" and "probability" are interchangeable. So, in normal conversation, it makes sense to say "the likelihood of weighing something between 23 and 35 grams is X". So that's OK. However, the mathematical definition restricts it to a single point. So when we are deriving things we have to use the strict, mathematical definition. p.s. Thank you so much for supporting StatQuest!!! BAM!

[@jabroomunda]

Great work done till this point. Videos are great and reflect meticulous effort. However it seems we are multiplying oranges and apples in the hope of getting strawberries. I have searched lot of famous books but never seen anyone plugging in numbers into f(x) equation of normal or exponential or any continuous function in the hope of getting single discrete value. Infact we always take integral and put in limits to get probability of a range of values. Of x and that is F(x).

[@jabroomunda]

@@statquest single point is discrete

[@kaczucha3able]

Hello! I'm grinding for my categorical data analysis exam (what doesnt set me in the best mood) and have to say that the song at the beginning made me feel slightly better

[@statquest]

bam! :)

[@aoihana1042]

BAM! Thank you Josh, you explain concepts with such clarity and ease!

[@gr4707]

This is so good. I’m looking to understand likelihood estimation function and just from this deep yet simple explanation I can guess what MLE is all about. Thanks!

[@statquest]

bam! :) If you want to see some examples, see: kzbin.info/www/bejne/pmS3XpKCgtepeMU kzbin.info/www/bejne/ep-Zk2yceK6Ipq8

[@FariborzGhavamian]

This was a very clean explanation of probability and likelihood. Thanks!

[@statquest]

Thank you! :)

[@TheAathi6]

Best explanation I have seen of probability and likelihood. Thank you so much..

[@statquest]

Glad it was helpful!

[@ryanal9866]

This is the best explanation I've ever seen! and I like your intro song as well!

[@statquest]

Hooray! :)

[@surbhimishra6795]

StatQuest make me feel soooooooooo happy 😊, thank you statQuest team 💜

[@statquest]

Hooray! BAM! :)

[@samirajodeir1285]

Thanks for this video. I'm a little confused about what you have mentioned about probability. You mentioned that probability is the area under the curve of distribution for a given interval. However if data is only a single point, the area is zero and it would contradict with this equation L(parameters; data) = P(data; parameters)

[@statquest]

For continuous data, likelihoods do not equal probabilities. This is only the case for discrete data.

[@aldairjimenez1101]

I must confess that I had a hard time understanding it too. (not knowing English is part of it, I've been playing the second video of the logistic regression series for more than 10 times) I think probability is when you evaluate the integral of the function in a certain range. And likelihood is when you evaluate the function at that point.

[@alifirhas3550]

The way of you speaking is very similar to Baldi in Baldi's Basics in Education and Learning. Which makes me terrified some times, but i'm generally more terrified how rapid i learn watching your videos. Thank you.

[@statquest]

bam!

[@TheAmateurGuitarist]

Bumped into this video, and glad I did! Please make a video using a discrete distribution. That'll really help differentiate between likelihood and probability. The problem with Y values being in a continuous domain is that, by definition, we'll always have to just say that the P(mouse weight = 32) = 0, and there ends any scope for comparing it to L(32) :-)

[@ln2deep]

Likelihood involves an existing model of data (the parameters) and some other data you want to evaluate your model on. Probability is just a model of data. They are functionally very similar but semantically different. The likelihood is how well your model fits some data. This uses the parameters in the same way you would when calculating probabilities. In both cases you are using the model to measure probability but what you do with those measurements is different. E.g you want probabilities to sum to 1 across the whole domain but you can measure an arbitrary number of data points for likelihood which can be unnormalised and you just want that number to go up when fitting the model to the data (make the data more likely under the parameters by changing the parameters). The conditional notation (x|y) is standard but can be confusing because in both cases the operation being performed is functionally very similar and the idea of predicting parameters from data is not intuitive. In both cases you evaluate some values of the domain of the probability distribution given by the parameters.

[@jojomojojones]

You get an automatic like just for the intro! Thanks for the video.

[@statquest]

Hooray!!!! You're welcome. :)

[@MrSpiritmonger]

this guy is smart and he is great at explaining things. he is a true national treasure.

[@statquest]

Thanks! :)

[@trilisser]

Thank you man, THANKS A LOT seriously. Finally I got it, omg

[@statquest]

Hooray!!! That's awesome! :)

[@elzilcho222]

When he said mouse weights, I imagined little dumbbells that mice lift at the gym

[@statquest]

:)

[@paulburger9904]

Wish I had seen this before I made my Baysian classifier. Thanks a lot for a great video!

[@LeCoolCroco]

Paul Burger why should someone cresate a NB classifier if there are plenty of them?

[@harpoon2445]

Probability is the area under a probability density function and represents the fraction of the times that a random draw would fall in that range, while likelihood is the value of the density function for one single event. Likelihood is used to estimate an unknown distribution, given a series of random draws from that distribution. You would solve for the parameters of the distribution the give the highest likelihood for the values that were drawn.

[@possiblypoet]

Starts at 0:32

[@statquest]

Noted

[@urjaswitayadav3188]

Thanks Joshua! I love your video series on probability and likelihood :)

[@prithviabilash7713]

When he says "BAM", that's when I remember to press "Like"

[@statquest]

BAM! :)

[@kenc00l]

Loved the content. Just a info for you to store in your stats that may or may not help. The pure white background burned my eyes because I was watching in the dark.

[@statquest]

noted

[@DmGrass]

I am a little bit confused concerning the second examle because this is probability density function, not cumulative distribution function. Probability density function has probability density (not probability itself) on vertical axis. So why did you conclude that likelihood is 0,12? In my opinion, this is probability density. In order to see likelihood we have to swich to cumulative distribution function and look what Y-value correspondes to 34 grams.

[@statquest]

The reason why we use a probability density function (PDF) is that a very large number, like 1,000,000 grams should have a very low likelihood - and the PDF ensures that is the case. If we used a cumulative density function (CDF) then the likelihood would be very large for a crazy large number, and that doesn't make sense.

[@Maha_s1999]

In all likelihood you may not fully understand the difference between probability density functions and cumulative density functions :-/

[@quAdxify]

That did actually also confuse me quite a bit at first as I thought the same, why is he describing the pdf. However, the thing is that normally you consider not just one sample but numerous, which form a product and that is also where it becomes clear what the likelihood is. I would suggest to maybe use multiple data points in the explanation since that is also how you are going to encounter it in most text books.

[@statquest]

@@quAdxify That's a good idea, and that's what I have in all of the videos that show "likelihood in action", for the exponential, binomial and normal distribution: kzbin.info/www/bejne/pmS3XpKCgtepeMU kzbin.info/www/bejne/anyuh2yvj6iig5Y kzbin.info/www/bejne/ep-Zk2yceK6Ipq8

[@hienthienthan2000]

Note that likelihood=0.12 doesn't mean that, given the observed data, those parameters have 12% of being the true parameters. The likelihood, in this case, just has a relative meaning. The degree to which data supports one parameter value versus another is measured by their likelihood ratio. To prove why PDF can be used as the "likelihood" and why maximizing likelihood is a good strategy for estimating distribution parameters is a different story (e.g., we must prove that maximizing the "likelihood" is equivalent to maximizing the PDF, and the parameter estimated by maximizing likelihood converges to the true parameters exponentially when the number of observed data point increases) In different foundations of statistics, the likelihood can mean different things. In Bayes inference, the likelihood has an absolute probability meaning, which says that "Given the parameter is true, what is the probability that I can observe this data".

[@palashsharma891]

I came here after watching a 3Blue1Brown video on probability distribution. This video really made me understand that one better. Thanks!

[@statquest]

Hooray! :)

[@vietta9204]

Holy sh*t! My head blown twice! Double BAM!!!

[@statquest]

Hooray! :)

[@Maha_s1999]

Excellent!! A lot of people are confused between likelihood and density functions. This makes it crystal clear. BAM! Subbed:-)

[@statquest]

Awesome!!! Thanks so much! :)

[@Bulbophile]

Sound track needed throughout

[@Francis-gg4rn]

Amazing videos, can you do a playlist on bayesian statistics?

[@choi77770]

This is the best explanation i've seen ever

[@statquest]

Thanks!

[@JustinShaedo]

The likely hood that this video labeled the Y axis is zero. The probability that this video labeled the Y axis is also zero.

[@fardaddanaeefard8247]

I wish i'd known you sooner, keep up the good work!

[@statquest]

Thanks!

[@domjervis]

Couldn't help but type in Comment #300 I would have LOVED to be a Mathematician or a Statistician. But had to give up on that when I realized that I didn't have quite the "Talent Level" that my peers who were going in that direction had. Paul Erdos I'm not. A friend told me (please understand that this was in the mid 70s), "You're going to need AT LEAST a Masters Degree before you can go out and beg for a job. And in all likelihood, not only will you will need to write a Thesis to get that Degree, but you're going to have to pick a topic VERY Soon after you start your Masters Studies AT THE LATEST or you will be light-years behind your classmates. Most of them will have chosen their Thesis Topic during their Undergraduate days." The only topic I can recall having had Any interest in at that time was the Navier-Stokes Equations. But, I have seen where so-called "Authorities" argue about whether this is a physics or a math Equation. So much for that. Also, tried to read background material on the Hodge Conjecture and it might as well have been written in Sanskrit. Also, I was told, "If you can't get a job as a Mathematician or a Statistician, you can always be a teacher." Yeah right... I can honestly say that I never had even ONE teacher that "inspired" me in any Method, Manner or Fashion. And the number of teachers I would have loved to hire the Columbine Boys to "take care of" is Easily in two digits. So I sure as heck wasn't going to become one of them. Lastly, given my Life-long Hatred of school in general (me and Evariste Galois, among others), I saw that going into Accounting was a viable alternative, in that I was able to get a job with just the (then) four-year Bachelors Degree. The day I put all school in the rear-view mirror for Life, I remember saying, "This is how prisoners who just got paroled must feel." All that aside, to this day Math and Statistics remain two of my favorite hobbies. Since I was Lucky and Blessed enough to have been able to retire five years ago at age 55, I have all day, every day, to do what I LIKE to do, rather than what I HAD to do to survive. GREAT Video! Thank you, Sir! All Best!

[@ReTr093]

Funny how things changed. Statisticians get hired straight out of school now,and no way in hell it's a teaching gig.

[@domjervis]

@@ReTr093 That's good to know and I am happy for each and every one of them. But I am curious. Do you know if the typical requirement for getting job as a statistician is a Masters Degree? Or can they become employed with a Bachelors Degree? Thank you for your response. All Best!

[@BoHorror]

Probability is about predicting future outcomes given a known model. Likelihood is about evaluating how well a model explains observed data. • Probability: “Given a fair coin, what’s the chance of flipping heads?” (Forward-thinking-you know the coin, you predict the result). • Likelihood: “I flipped heads 8 times out of 10-how likely is it that my coin is fair?” (Backward-thinking-you have the result, you assess the model). Key Difference: • Probability deals with possible outcomes from a known process. • Likelihood measures how well a given process explains observed outcomes.

[@abhishekchandrashukla3814]

Statsquest makes me feel so happy So very very very very very very very very very happy

[@statquest]

:)

[@somdubey5436]

Thanks!

[@statquest]

Wow!!! Thank you so much for your support! BAM! :)

[@erikthegodeatingpenguin2335]

So the likelihood is somewhat like the derivative of the probability?

[@phunmaster2000]

no, it's just the value of the distribution at that point, not the slope of the distribution

[@burkean]

It sure seems that the probability is the integral of the likelihood.

[@hitherthither5712]

Best video I have seen till now on 'Probability Vs Likelihood', Thanks!

[@HH3222]

Finally someone from the USA using metric measurements.

[@IslamAshraf-u6h]

Thank you for keeping things very clear!❤

[@statquest]

Any time!

[@alsnyder1660]

I would rather seen an apples to apples discussion. You showed probability of a RANGE of mouse weight but showed likelihood of one SPECIFIC mouse weight.

[@statquest]

Probability is area under the curve. The area for a specific point is 0, because a rectangle with 0 width has area 0 * height = 0. Thus, when we want to talk about a specific mouse weight, we talk about the likelihood. If we want to talk about a range of values, we talk about probability.

[@qvourek]

Triple-bam…

[@poiewhfopiewhf]

thats the thing, is when it got into the nitty gritty of how probability was calculated before stating what likelihood was it made it not crystal clear that the distinction requires no math at all and is as simple as you stated it in this comment

[@AF-mw8gy]

@@poiewhfopiewhf that’s so interesting, because to me that was very clear from the video. Just goes to show how different people can pick up things so differently. Sure makes teaching hard.

[@HazemAzim]

Very interesting and nice perspective on probability vs likelihood .. that is new !

[@statquest]

Glad you liked it!

[@sonalidasgupta3562]

The likelihood part confused me...what here is shown as likelihood sounds more like hypth testing

[@statquest]

The best way to understand likelihood is to see it in action. Check out how likelihood is used to find the optimal exponential distribution given some data: kzbin.info/www/bejne/pmS3XpKCgtepeMU

[@yqisq6966]

It's best understood through conditional probability. The symbol P(x|y) means the "probability density of x conditioned on y", and it is at the same time the "likelihood of y".

[@roxm4356]

You are the best and easiest in statistics

[@statquest]

Thank you! :)

[@qingchen2510]

As you said ，so clearly explained，Thank you very much.

[@statquest]

You are welcome!!! I'm glad you like the video. :)

[@Exceltech810]

Great explanation. Please shared more videos for statistics in grad level. Thanks!

[@statquest]

Will do!

[@mAcCoLo666]

Strange, almost every book I've read so far talk of P(data|distribution) as likelihood, and P(distribution|data) as posterior. Am I missing something here? 🤔

[@statquest]

That is very interesting. The second part, P(distribution | data), is in fact a posterior, as you suspect. The "P" is the important part. It tells you to integrate the function. If it were "L", then we would a likelihood, and that would tell you evaluate the function a specific point. The first part, however, P( data | distribution) being called a likelihood is confusing. Even Bayesian folks tend to observe the "P" means "probability" and "L" means "likelihood" convention. That said, in Baysian statistics, you'll see likelihood functions written like this L( data | distribution). However, in this case, they are calculated just like L( distribution | data). The difference being that Bayesians let the parameters be random variables, and non-Bayesians only let the data be random variables.

[@ronaldjensen2948]

P(distribution|data) = [P(data|distribution) * P(distribution)] / P(data) or in Bayesian Terms posterior = likelihood * prior. In the likelihood function we are given a fixed data set (the measurement) and we are postulating the distribution that data set came from. This is what Josh says in the video. Also, P(data) is a constant to make the posterior integrate to 1.

[@AshishKumar-xx3dx]

as usual amazing videos by StatQuest

[@statquest]

Glad you like them!

[@not_a_human_being]

great vid, but I almost feel that it would've been much more clear with discrete distribution.

[@statquest]

It's true - a discrete distribution would be a little easier to understand, but most people do t-tests, which are continuous, so I figured I'd start there. however, I may do another video that shows the discrete version.

[@luisluiscunha]

Why do people down vote this? Really... Great job, Josh. Thank you very much. Kudos to you, and let Karma take care of the rest.

[@statquest]

:)

[@digital_harry]

Those are outliers, highly deviated from the mean.

[@Larimerst]

Yes! I'm finding this funny, fascinating and awesome! But I am very high.

[@JM-us3fr]

Very interesting! I wish I could have taken more stats in my math graduate program. I’ve definitely been confusing these two

[@statquest]

bam!

[@georgesmith3022]

i thought that the probability of a certain value in continous distribution is always 0. you dont have discrete weights like 32, 33 etc, but 32.00000001 etc. the probability of a mouse being exactly 32 is zero.

[@statquest]

That is exactly right. However, the likelihood for a single point is not zero. The reason for this might be more obvious if you saw likelihoods in action. Here's a video that shows how likelihoods are used to estimate parameters for the exponential distribution: kzbin.info/www/bejne/pmS3XpKCgtepeMU

[@georgesmith3022]

@@statquest ok I meant it tends towards 0. So even 0.1 is a big value. But i believe u know better math than me.

[@statquest]

@@georgesmith3022 No, it's zero. For example, the area of a rectangle that has 0 width is 0. So the area under the curve of a continuous statistical distribution, like the normal distribution, with 0 width is 0.

[@anastasiahaley6391]

You teaching style is amazing! Could you, please, make a video on Multiple Correspondence Analysis?

[@statquest]

I'll keep it in mind.

[@bakedutah8411]

Shyeah, right! Try telling this to the editors of the Wikipedia article on Probability.

[@chyldstudios]

the clearest explanation of the connection between likelihood and probability. more videos!

[@flycanfly]

4:39 Hurray with no soul

[@statquest]

Oh well. :)

[@debatradas1597]

Thank you so much... I'm glad I got to learn something new today

[@statquest]

Thanks!

[@liamhoward2208]

Anybody else think he was talking about tiny weights that you put on a scale when he said mouse weights? Lmao

[@statquest]

I love it! :)

[@jaijeffcom]

I got another BAMM for you. Bam, subscribed! That was a vivid and accessible illustration. I never have to fret over this distinction again. Now I want to see the rest of these videos. Yay.

[@statquest]

:)

[@MrCmon113]

That still makes "likelihood" a probability though.

[@anaccountmusthaveaname9110]

no

[@empireempire3545]

no

[@ronaldjensen2948]

Not exactly. Probability is the integral from a to b of f(x)dx, likelihood is just f(x). If you remember calculus, any integral from a to a is zero, even if the interior function is not.

[@MrCmon113]

@@ronaldjensen2948 I've randomly stumbled on the same video again and yes, it says that likelihood is the PDF. I don't know how me from ten months ago arrived at his conclusion.

[@faridrezanajafi9565]

Very simple description of probability and likelihood. Well done!

[@statquest]

Thank you very much! :)