Maximum Likelihood Estimation

Maximum likelihood estimation (MLE) picks the parameter values that make the data you actually observed most probable. You write down a model with unknown knobs, then turn the knobs until the model says “yes, data like this is exactly what I’d expect.”

It is the workhorse behind much of modern statistics and machine learning — fitting a logistic regression (邏輯迴歸), for instance, is maximum likelihood under the hood. Two cautions: the answer is only as good as the model you assumed (wrong model, confidently wrong estimate), and with little data it can overfit, which is one motivation for adding a Bayesian prior.