Probability is not Likelihood. Find out why!!!

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  • เผยแพร่เมื่อ 17 มิ.ย. 2024
  • NOTE: This video was originally made as a follow up to an overview of Maximum Likelihood • Maximum Likelihood, cl... . That video provides context that gives this video more meaning.
    Here's one of those tricky little things, Probability vs. Likelihood. In common conversation we use these words 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. The StatQuest gives you visual images that make them both easy to remember so you'll always keep them straight.
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ความคิดเห็น • 1.1K

  • @suivzmoi
    @suivzmoi 5 ปีที่แล้ว +1397

    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
      @statquest  5 ปีที่แล้ว +153

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

    • @mohamedrefaat197
      @mohamedrefaat197 5 ปีที่แล้ว +28

      Thanks for clarification

    • @LuisPereira-bn8jq
      @LuisPereira-bn8jq 5 ปีที่แล้ว +32

      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
      @dreaminglucid1316 5 ปีที่แล้ว +25

      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
      @suivzmoi 5 ปีที่แล้ว +30

      @@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

  • @BulkySplash169
    @BulkySplash169 2 ปีที่แล้ว +126

    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
      @statquest  2 ปีที่แล้ว

      Thanks!

    • @ExistenceUniversity
      @ExistenceUniversity ปีที่แล้ว +1

      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.

  • @statquest
    @statquest  2 ปีที่แล้ว +1

    Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/

  • @zerosiii
    @zerosiii 6 ปีที่แล้ว +182

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

  • @graymars1097
    @graymars1097 3 ปีที่แล้ว +6

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

  • @patheddles4004
    @patheddles4004 2 ปีที่แล้ว +6

    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. :-)

  • @ob96275
    @ob96275 6 ปีที่แล้ว +4

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

  • @Hamromerochannel
    @Hamromerochannel 2 ปีที่แล้ว +10

    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
      @statquest  2 ปีที่แล้ว +4

      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.

  • @skandagurunathanr4795
    @skandagurunathanr4795 4 ปีที่แล้ว +4

    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
      @statquest  4 ปีที่แล้ว +1

      Awesome! :)

  • @mastermike890
    @mastermike890 6 ปีที่แล้ว +450

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

    • @ionahrapsa5146
      @ionahrapsa5146 5 ปีที่แล้ว +5

      Very well put

    • @benphua
      @benphua 5 ปีที่แล้ว +1

      Haha agreed!

    • @nathanlewis42
      @nathanlewis42 5 ปีที่แล้ว +5

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

    • @annapeng88
      @annapeng88 4 ปีที่แล้ว +1

      Totally agree Bob Ross of Statistics haha

    • @immanuelkant7895
      @immanuelkant7895 3 ปีที่แล้ว

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

  • @elderhiker7787
    @elderhiker7787 2 ปีที่แล้ว +31

    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
      @statquest  2 ปีที่แล้ว +2

      Thank you very much! :)

  • @missregita
    @missregita 6 ปีที่แล้ว +9

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

  • @sarrae100
    @sarrae100 4 ปีที่แล้ว +15

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

    • @statquest
      @statquest  4 ปีที่แล้ว +2

      Thank you! :)

  • @aoihana1042
    @aoihana1042 6 ปีที่แล้ว +8

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

  • @abdallahbahyabdelazimothma8359
    @abdallahbahyabdelazimothma8359 4 ปีที่แล้ว +34

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

    • @statquest
      @statquest  4 ปีที่แล้ว +1

      Thank you! :)

  • @gurditsinghchandok1641
    @gurditsinghchandok1641 3 ปีที่แล้ว +10

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

    • @statquest
      @statquest  3 ปีที่แล้ว +1

      Glad it was helpful!

    • @morganjones7428
      @morganjones7428 2 ปีที่แล้ว +1

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

  • @chiragvartak5658
    @chiragvartak5658 3 ปีที่แล้ว +9

    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
      @statquest  3 ปีที่แล้ว +2

      Thanks! :)

  • @MadhushreeSinha
    @MadhushreeSinha 4 ปีที่แล้ว +48

    statquest makes feel very very very happy indeed!

    • @statquest
      @statquest  4 ปีที่แล้ว +3

      Hooray!!! :)

  • @jaijeffcom
    @jaijeffcom ปีที่แล้ว +2

    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
      @statquest  ปีที่แล้ว

      Wow, thank you!

  • @hitherthither5712
    @hitherthither5712 4 ปีที่แล้ว +2

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

  • @sarthakdua3234
    @sarthakdua3234 4 ปีที่แล้ว +9

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

    • @statquest
      @statquest  4 ปีที่แล้ว +1

      Hooray! :)

  • @becauserocks.5784
    @becauserocks.5784 5 ปีที่แล้ว +5

    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
      @statquest  5 ปีที่แล้ว +1

      Hooray! :)

  • @xiukuiji747
    @xiukuiji747 2 ปีที่แล้ว +2

    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
      @statquest  2 ปีที่แล้ว

      Awesome, thank you!

  • @jaijeffcom
    @jaijeffcom 3 ปีที่แล้ว +1

    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.

  • @michaelduncan5805
    @michaelduncan5805 4 ปีที่แล้ว +11

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

  • @urjaswitayadav3188
    @urjaswitayadav3188 6 ปีที่แล้ว +3

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

  • @nikitaarora347
    @nikitaarora347 3 ปีที่แล้ว +2

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

  • @lazregmohamedlamine4847
    @lazregmohamedlamine4847 6 ปีที่แล้ว +2

    thank you, you upload this statquest in the right time!!,best

  • @shenzou4778
    @shenzou4778 3 ปีที่แล้ว +3

    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
      @statquest  3 ปีที่แล้ว

      Thank you very much! :)

  • @ryanal9866
    @ryanal9866 5 ปีที่แล้ว +3

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

  • @Nakameguro97
    @Nakameguro97 4 ปีที่แล้ว +2

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

    • @statquest
      @statquest  4 ปีที่แล้ว

      Thank you! :)

  • @EnlightenNook
    @EnlightenNook 3 ปีที่แล้ว +2

    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
      @statquest  3 ปีที่แล้ว

      Thank you! :)

  • @trilisser
    @trilisser 5 ปีที่แล้ว +13

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

    • @statquest
      @statquest  5 ปีที่แล้ว

      Hooray!!! That's awesome! :)

  • @FariborzGhavamian
    @FariborzGhavamian 5 ปีที่แล้ว +3

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

    • @statquest
      @statquest  5 ปีที่แล้ว

      Thank you! :)

  • @sannwailhyan5113
    @sannwailhyan5113 ปีที่แล้ว +1

    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.

  • @chyldstudios
    @chyldstudios 6 ปีที่แล้ว

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

  • @justtoleavecomments3755
    @justtoleavecomments3755 5 ปีที่แล้ว +10

    Actually makes things so much more intuitive, thank you!

  • @paulburger9904
    @paulburger9904 5 ปีที่แล้ว +3

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

    • @LeCoolCroco
      @LeCoolCroco 4 ปีที่แล้ว

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

  • @sachinsh9398
    @sachinsh9398 6 ปีที่แล้ว +1

    Just awesome !!! The concepts are made so so simple to understand. Big thumbs up to you :)

    • @statquest
      @statquest  6 ปีที่แล้ว

      Hooray!!! I'm glad you like the video! :)

  • @tunneloflight
    @tunneloflight 2 ปีที่แล้ว

    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.

  • @ThotWalter
    @ThotWalter 4 ปีที่แล้ว +5

    I love this channel!!!

    • @statquest
      @statquest  4 ปีที่แล้ว +2

      Thank you! :)

  • @TheAmateurGuitarist
    @TheAmateurGuitarist 5 ปีที่แล้ว +9

    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) :-)

  • @palashsharma891
    @palashsharma891 4 ปีที่แล้ว +2

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

    • @statquest
      @statquest  4 ปีที่แล้ว +1

      Hooray! :)

  • @Stew282
    @Stew282 2 ปีที่แล้ว +1

    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
      @statquest  2 ปีที่แล้ว

      Glad it helped! :)

  • @JMRG2992
    @JMRG2992 4 ปีที่แล้ว +11

    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
      @statquest  4 ปีที่แล้ว +7

      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
      @diegofabianledesmamotta5139 ปีที่แล้ว +1

      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
      @misiek_xp4886 ปีที่แล้ว +2

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

  • @qingchen2510
    @qingchen2510 6 ปีที่แล้ว +7

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

    • @statquest
      @statquest  6 ปีที่แล้ว +1

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

  • @se123acabaron
    @se123acabaron 5 ปีที่แล้ว +1

    Brilliant! Thank you very much for this easy, visual explanation.

    • @statquest
      @statquest  5 ปีที่แล้ว

      Hooray! :) You're welcome! :)

  • @surbhimishra6795
    @surbhimishra6795 2 ปีที่แล้ว +2

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

    • @statquest
      @statquest  2 ปีที่แล้ว

      Hooray! BAM! :)

  • @jojomojojones
    @jojomojojones 5 ปีที่แล้ว +3

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

    • @statquest
      @statquest  5 ปีที่แล้ว

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

  • @akhilachillara1845
    @akhilachillara1845 4 ปีที่แล้ว +24

    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
      @statquest  4 ปีที่แล้ว +25

      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
      @jabroomunda 2 ปีที่แล้ว +1

      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
      @jabroomunda 2 ปีที่แล้ว

      @@statquest single point is discrete

  • @PedroRibeiro-zs5go
    @PedroRibeiro-zs5go 5 ปีที่แล้ว +2

    Man, right to the point, as usual!! Thanks!!!

    • @statquest
      @statquest  5 ปีที่แล้ว

      Thank you! :)

  • @user-vc8qq1ut1m
    @user-vc8qq1ut1m 7 หลายเดือนก่อน +1

    Thank you for keeping things very clear!❤

    • @statquest
      @statquest  7 หลายเดือนก่อน

      Any time!

  • @Francis-gg4rn
    @Francis-gg4rn 5 ปีที่แล้ว +3

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

  • @susovan97
    @susovan97 5 ปีที่แล้ว +3

    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.

  • @Maya_s1999
    @Maya_s1999 5 ปีที่แล้ว +1

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

    • @statquest
      @statquest  5 ปีที่แล้ว

      Awesome!!! Thanks so much! :)

    • @Bulbophile
      @Bulbophile 5 ปีที่แล้ว

      Sound track needed throughout

  • @aishah8398
    @aishah8398 2 ปีที่แล้ว +1

    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

  • @vietta9204
    @vietta9204 5 ปีที่แล้ว +7

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

  • @bakedutah8411
    @bakedutah8411 5 ปีที่แล้ว +3

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

  • @madhubagroy
    @madhubagroy 2 ปีที่แล้ว +1

    Top-notch! So impressed by your explanations. Thank you!

  • @TheAathi6
    @TheAathi6 ปีที่แล้ว +1

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

    • @statquest
      @statquest  ปีที่แล้ว

      Glad it was helpful!

  • @DmGrass
    @DmGrass 5 ปีที่แล้ว +23

    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
      @statquest  5 ปีที่แล้ว +9

      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.

    • @Maya_s1999
      @Maya_s1999 5 ปีที่แล้ว +8

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

    • @quAdxify
      @quAdxify 5 ปีที่แล้ว +3

      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
      @statquest  5 ปีที่แล้ว +1

      @@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:
      th-cam.com/video/p3T-_LMrvBc/w-d-xo.html
      th-cam.com/video/4KKV9yZCoM4/w-d-xo.html
      th-cam.com/video/Dn6b9fCIUpM/w-d-xo.html

    • @hienthienthan2000
      @hienthienthan2000 5 ปีที่แล้ว +4

      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".

  • @pictureworksdenver
    @pictureworksdenver 5 ปีที่แล้ว +6

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

  • @nataliatenoriomaia1635
    @nataliatenoriomaia1635 4 ปีที่แล้ว +1

    I love your videos, they are so therapeutic.

    • @statquest
      @statquest  4 ปีที่แล้ว +1

      Thank you very much! :)

  • @lakshmiganaprasadantervedi3865
    @lakshmiganaprasadantervedi3865 4 ปีที่แล้ว +1

    Thanks Josh! This is exactly what I needed

    • @statquest
      @statquest  4 ปีที่แล้ว

      Awesome!!! :)

  • @samirajodeir1285
    @samirajodeir1285 3 ปีที่แล้ว +6

    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
      @statquest  3 ปีที่แล้ว +8

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

    • @aldairjimenez1101
      @aldairjimenez1101 ปีที่แล้ว

      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.

  • @domjervis
    @domjervis 5 ปีที่แล้ว +6

    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
      @ReTr093 5 ปีที่แล้ว

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

    • @domjervis
      @domjervis 5 ปีที่แล้ว

      @@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!

  • @df4250
    @df4250 5 ปีที่แล้ว +1

    Beautifully explained! Excellent job.

    • @statquest
      @statquest  5 ปีที่แล้ว

      Thank you! :)

  • @gr4707
    @gr4707 ปีที่แล้ว +1

    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
      @statquest  ปีที่แล้ว

      bam! :) If you want to see some examples, see: th-cam.com/video/p3T-_LMrvBc/w-d-xo.html th-cam.com/video/Dn6b9fCIUpM/w-d-xo.html

  • @simonty1811
    @simonty1811 5 ปีที่แล้ว +7

    did Donald Trump write your lyrics? It was very very very good. Studying stats from Sydney. I come here because I don't understand uni my lectures :(

    • @statquest
      @statquest  5 ปีที่แล้ว +1

      Hooray! I'm glad to hear that the video was helpful. :)

  • @not_a_human_being
    @not_a_human_being 5 ปีที่แล้ว +4

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

    • @statquest
      @statquest  5 ปีที่แล้ว

      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.

  • @fardaddanaeefard8247
    @fardaddanaeefard8247 2 ปีที่แล้ว +1

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

  • @himanshumaithani8499
    @himanshumaithani8499 3 หลายเดือนก่อน +1

    Very indepth explanation with visualizations and illustrations. I like the way you teach, brother. Keep it up...❤

    • @statquest
      @statquest  3 หลายเดือนก่อน

      Thank you so much 😀

  • @HH3222
    @HH3222 5 ปีที่แล้ว +3

    Finally someone from the USA using metric measurements.

  • @sonalidasgupta3562
    @sonalidasgupta3562 5 ปีที่แล้ว +9

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

    • @statquest
      @statquest  5 ปีที่แล้ว +1

      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: th-cam.com/video/p3T-_LMrvBc/w-d-xo.html

    • @yqisq6966
      @yqisq6966 5 ปีที่แล้ว

      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".

  • @debatradas1597
    @debatradas1597 3 ปีที่แล้ว +1

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

  • @PhongNguyen-nv7jj
    @PhongNguyen-nv7jj 2 ปีที่แล้ว +1

    Perfectly explained! Thank you.

  • @erikthegodeatingpenguin2335
    @erikthegodeatingpenguin2335 5 ปีที่แล้ว +3

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

    • @phunmaster2000
      @phunmaster2000 5 ปีที่แล้ว

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

    • @burkean
      @burkean 5 ปีที่แล้ว

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

  • @mAcCoLo666
    @mAcCoLo666 5 ปีที่แล้ว +3

    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
      @statquest  5 ปีที่แล้ว +1

      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
      @ronaldjensen2948 5 ปีที่แล้ว

      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.

  • @lilmoesk899
    @lilmoesk899 6 ปีที่แล้ว

    great stuff as usual!

  • @faridrezanajafi9565
    @faridrezanajafi9565 4 ปีที่แล้ว +1

    Very simple description of probability and likelihood. Well done!

    • @statquest
      @statquest  4 ปีที่แล้ว

      Thank you very much! :)

  • @liamhoward2208
    @liamhoward2208 5 ปีที่แล้ว +5

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

    • @statquest
      @statquest  5 ปีที่แล้ว +1

      I love it! :)

  • @justinking5964
    @justinking5964 4 ปีที่แล้ว +3

    God ! So hard have I been through, to finally find a intelligent guy to know probability.Hi Josh Starmer Can I talk to you in private? Can I make friends with you.

    • @justinking5964
      @justinking5964 4 ปีที่แล้ว

      Can I talk to you in private? Can I make friends with you.
      edenlove 828 hotmail.

  • @BiranchiNarayanNayak
    @BiranchiNarayanNayak 5 ปีที่แล้ว +2

    Excellent tutorial....love it.

    • @statquest
      @statquest  5 ปีที่แล้ว

      Thank you! :)

  • @MrSpiritmonger
    @MrSpiritmonger 4 ปีที่แล้ว +2

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

  • @georgesmith3022
    @georgesmith3022 5 ปีที่แล้ว +7

    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
      @statquest  5 ปีที่แล้ว +4

      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: th-cam.com/video/p3T-_LMrvBc/w-d-xo.html

    • @georgesmith3022
      @georgesmith3022 5 ปีที่แล้ว +1

      @@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
      @statquest  5 ปีที่แล้ว +3

      @@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.

  • @jms019
    @jms019 5 ปีที่แล้ว +18

    The probability of a mouse weighing exactly 34g Is IS ZERO

    • @haraldkeilhack4266
      @haraldkeilhack4266 5 ปีที่แล้ว +4

      Right! It seems he talks about the probability that the mouse has a weight between 33,5 and 34,499999 g. And then we talk again about an area under the graph as before. So the whole video is a fail.

    • @MrCmon113
      @MrCmon113 5 ปีที่แล้ว

      Yeah you need to define conditional probabilities differently for that case.

    • @xnoreq
      @xnoreq 5 ปีที่แล้ว +2

      Yes but he's not talking about the probability of the mouse weighing exactly 34g. The mouse weighs 34g. It's a given. A data point.
      The question is how likely this is given a distribution. That's what the likelihood is for.

    • @MrYouzilyj621
      @MrYouzilyj621 5 ปีที่แล้ว +2

      he never said probability, he said likelihood.

    • @wernersmidt3298
      @wernersmidt3298 5 ปีที่แล้ว

      You are absolutely correct, but please refer to the title of the video. *the likelihood of the **_distribution_** (with the stated parameters) given you had a mouse of 34g*

  • @humanintheloop
    @humanintheloop 4 ปีที่แล้ว +1

    great explanation, thanks

  • @BChow-td7qh
    @BChow-td7qh 3 ปีที่แล้ว +1

    I really like your way of presenting the concept in great detail even denote the given sign.
    It's great for people at the entry-level. Thumps up~~

    • @statquest
      @statquest  3 ปีที่แล้ว

      Thank you very much!

  • @MrCmon113
    @MrCmon113 5 ปีที่แล้ว +8

    That still makes "likelihood" a probability though.

    • @anaccountmusthaveaname9110
      @anaccountmusthaveaname9110 5 ปีที่แล้ว +2

      no

    • @empireempire3545
      @empireempire3545 5 ปีที่แล้ว +1

      no

    • @ronaldjensen2948
      @ronaldjensen2948 5 ปีที่แล้ว

      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
      @MrCmon113 4 ปีที่แล้ว

      @@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.

  • @lakshaydulani
    @lakshaydulani 6 ปีที่แล้ว +3

    Nice explanation but i m afraid i still dont understand whats likelihood..can somebody pls explain in plain words..josh has explained in terms of formula

    • @amerel-samman9929
      @amerel-samman9929 2 ปีที่แล้ว

      say you measure one mouse. ONLY one mouse. You get 34g. You know nothing about mice? according to your single experiment it is probably best to put the mean of mice around 34g because that gives the max likelihood for your experiment (i.e because the mean has highest probabilityy. For all you know now the mean is 34g and thats it but you only did 1
      now you go ahead and do 2 mass weights one at 34g and one happened to be at 30g. According to your original distribution where mean was at 34 this would not give maximum likelyhood because the mass at 30g is very little represented. You will have to shift your distributiion to MAXIMIZE likelihood. To maximize the probability of all measurements

  • @saurabhsharma8577
    @saurabhsharma8577 5 ปีที่แล้ว +1

    Hi, You are amazing. Keep making such good videos. It helps a lot in learning. Thank you.

  • @haroldsu1696
    @haroldsu1696 5 ปีที่แล้ว +2

    fantastic explain. Thank you !

    • @statquest
      @statquest  5 ปีที่แล้ว

      Thank you! :)

  • @RabidMortal1
    @RabidMortal1 5 ปีที่แล้ว +5

    I am slightly confused. I have always been taught that the likelihood of a model is the probability of the data given the model, but the notation uses is always in the form of P(Data | Model). this is the opposite of how the video is presenting it.

    • @statquest
      @statquest  5 ปีที่แล้ว

      Both the likelihood and probability use the same exact function, but they are used differently. When you calculate probability, you integrate the function, when you calculate likelihood, you evaluate it at specific points.

    • @RabidMortal1
      @RabidMortal1 5 ปีที่แล้ว +2

      @@statquest I think what it confusing is that the textbook definition of the likelihood function L can be written as a conditional probability P such that P(data|model)==L(model|data).

    • @statquest
      @statquest  5 ปีที่แล้ว +5

      @@RabidMortal1 If the distribution is discrete, like binomial, then P(data | model) == L(model | data). However, when the distribution is continuous, like a normal distribution, then P does not equal L. For more information, check out my videos where I show the likelihood function in action. First, here's how it works with a continuous distribution: th-cam.com/video/p3T-_LMrvBc/w-d-xo.html ...and here's how it works for a discrete distribution: th-cam.com/video/4KKV9yZCoM4/w-d-xo.html

    • @OKMathh
      @OKMathh 5 ปีที่แล้ว

      sometimes people use 'likelihood' to mean 'probability'. in the case you mentioned, it's actually mean 'probabiity'.

  • @kyjo72682
    @kyjo72682 5 ปีที่แล้ว +3

    That's weird. I think of those two words as synonyms. Your explanation would still make sense if you swapped the words. I think what you're describing is just a convention, not proper semantics.

    • @statquest
      @statquest  5 ปีที่แล้ว +4

      In normal conversation, those word are synonymous, but in statistics, they have well defined (and different) meanings. So it just depends on context. Usually there is no difference, but if you're doing statistics, they are different. For example, when people use "maximum likelihood" to solve a problem in statistics, that is very, very different from using "maximum probability".

  • @prithviabilash7713
    @prithviabilash7713 ปีที่แล้ว +2

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

  • @pietronickl8779
    @pietronickl8779 3 ปีที่แล้ว +1

    thanks for another intuitive and concise explanation!

    • @statquest
      @statquest  3 ปีที่แล้ว

      My pleasure!

  • @zofe
    @zofe 5 ปีที่แล้ว +3

    The likelihood of a point on a continuous line is epsilon of zero.

  • @eaglegrip6879
    @eaglegrip6879 5 ปีที่แล้ว +3

    Yeah, but what's mouse's name? And why do you have a mouse fetish?

    • @cosmonauta3038
      @cosmonauta3038 5 ปีที่แล้ว

      Jajaja he loves mouses but his stats videos are very nice.

  • @joshuadimick723
    @joshuadimick723 2 ปีที่แล้ว +2

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

    • @statquest
      @statquest  2 ปีที่แล้ว

      That's a great idea! BAM! :)

  • @AshishKumar-xx3dx
    @AshishKumar-xx3dx 3 ปีที่แล้ว +1

    as usual amazing videos by StatQuest

    • @statquest
      @statquest  3 ปีที่แล้ว +1

      Glad you like them!