Maximum Likelihood

Should’ve paid more attention in class…

Simple terms, Maximum Likelihood is a way to choose model parameters so that the data you observed would be as probable as possible under the model

So if you decide your data follows a Normal distribution, you’re assuming your data looks like a bell curve described by 2 parameters:

• mean $\mu$: the center of the bell
• standard deviation $\sigma$: how spread out it is

For proposed $\mu \text{ and }\sigma$, the Normal distribution assigns a probability density to each data point. The likelihood measures how well these parameters explain all the datapoints together

The MLE then chooses $\mu$ and $\sigma$ values that make the observed dataset fit the bell curve the best