StatQuest: Maximum Likelihood, clearly explained!!!


If you hang out around statisticians long enough, sooner or later someone is going to mumble “maximum likelihood” and everyone will knowingly nod. After this video, so can you!
Also, some viewers asked for a worked out example that includes the math. Here it is! (you may need to click on the “Show More” button below to see the link)

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0:00 Awesome song and introduction
0:34 Motivation for MLE
1:12 Overview of the Normal Distribution
2:06 Thinking about where to center the distribution
3:25 Using MLE to find the optimal location for the center
4:27 Using MLE to find the optimal standard deviation
5:19 Probability vs Likelihood

#statquest #MLE


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  1. You always disappointed me 🤗🤗hey do not be sad
    I mean I always thought before watch quest that I will comment my doubt after watching quest but I never found doubts 🤭so in this you made me disappointed🤭 very excellent content you makes 😘🥰🥰

  2. This is probably a naive question. But why do we need to find parameters of distribution when we can directly calculate them using observed data?

  3. so basically you are centering a normal distribution at each data point and checking for which maximizes the prob of the rest of the data…
    but my question is how to u figure out how to that it maxmixes prob at different because centering the data at different points will lead to different values of prob at different points.. so on what weight do we choose the dist

    Is is the prob at the point at which it is centered

  4. How does this differ, at least in the case of the normal distribution, from simply taking the mean & standard deviation of the data and using them as parameters for the distribution?

  5. the intro made my day man.I have a shit tone of assignments and i am low on time so really that little guitar gig made me smile.Also great work on the explanations.KEEP it up!!

  6. Really good! Made it a lot clearer!
    Just wondering how to understand this for phylogenetics. Does Maximum Likelihood analysis in constructing phylogenetic trees mean that you draw all the potential trees and fit a normal distribution to each tree being the "true tree" as you did in the video. So the maximum likelihood (the observation that explains the species data best) is the most likely phylogenetic tree that explains the species data?

  7. We have some data, we want to find the distribution that best bits this data.
    The distribution that has a mean that matches the mean of our data maximizes the likelihood of the data
    We keep shifting the mean of the distribution until we find a point that maximizes our likelihood of the data points. We find also the standard deviation that maximizes the likelihood of our data
    To mathematically find this pdf that best fits our data, sub in all our data points into the pdf (likelihood for all our data points is likelihood of one point x likelihood of next point etc) and then we differentiate partial differentiation wrt to the mean and standard deviation (in the case of normal pdf, which is parameterized by the mean and standard deviation)

  8. A very basic question — how do you decide the distribution of a dataset? In this case you assume it's normally distributed. Why it can't be like a gamma distribution? Is there a way to figure out which distribution we should work on?

  9. Is this why the “p(E|H)” component of Bayes rule is called the “likelihood”? I see the connection with “given a bunch of observed measurements” (from the “Terminology Alert” section), but not the part about it specifically refers to finding the optimal value for measures.

  10. Excellent video….loved the way you explained it. FINALLY!!!!! I understood what MLE actually means. Great work Josh! 🙂

  11. Damn, you know how to sing!!! Love the guitar too 🙂 Thank you, great explanation! I would love to have a Stat Quest on Group Sequential Testing (as opposed to Fixed sample size testing, my interest is in A/B testing)…

  12. Thank you very much for making such instructive video, it helps me a lot!!
    But when I learning video teaching about Maximum Likelihood, I am alway confused about the purpose of Maximum Likelihood, since we can already know the shape and position of a normal distribution depend on the mean and standard deviation, why should we use the Maximum Likelihood?

  13. Every time I listen to the intro I can imagine Phoebe singing it. Thanks for the explanation, your channel is the best I found about statistics on youtube and it's helping me analyse results for my thesis <3

  14. Hello ! Thank you for this video ! I have a question : at 3:29, this is the likehood of observing which data in particular on this y axis ?

  15. I think you're the king in machine learning and statistics on YouTube. Could you please make a playlist for deep learning as well ?


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