Maximum Likelihood, clearly explained!!!

StatQuest, it's bad to the bone. StatQuest, check it out. It's bad to the bone. Hello, and welcome to StatQuest. StatQuest is brought to you by the friendly folks in the genetics department at the University of North Carolina at Chapel Hill. Today, we're going to be talking about maximum likelihood. Let's say we weighed a bunch of mice.

The goal of maximum likelihood is to find the optimal way to fit a distribution to the data. There are lots of different types of distributions for different types of data. Here's a normal distribution. Here's what an exponential distribution looks like. And here's what a gamma distribution looks like. And there are many more.

The reason you want to fit a distribution to your data is it can be easier to work with, and it is also more general. It applies to every experiment of the same type. In this case, we think the weights might be normally distributed. That means we think it came from this type of distribution.

Normally distributed means a number of things. First, we expect most of the measurements, for example, mouse weights, to be close to the mean or average. And we see, lo and behold, in our data set, most of the mice weigh close to the average. We also expect the measurements to be relatively symmetrical around the mean.

Although the measurements are not perfectly symmetrical around the mean, they are not crazy skewed to one side, either. This is pretty good. Normal distributions come in all kinds of shapes and sizes. They can be skinny, medium, or large-boned. Once we settle on the shape, we have to figure out where to center the thing.

Is one location better than another? Before we get too technical, let's just pick any old normal distribution and see how well it fits the data. This distribution says, "Most of the values you measure should be near my average." The distribution's average is the black dotted line. In this case, that's different from the average of the actual