MLE

Introduction In modern Bayesian statistics, we often face posterior distributions that are difficult to compute. Let $p(z)$ be prior density and $p(x \mid z)$ be likelihood. The standard approach to compute posterior $p(z \mid x)$ is to use MCMC (like Metropolis-Hastings, Gibbs sampling and HMC).

TL;DR What are we actually doing on MLE? What is the motivation for the Maximum Likelihood Estimation? In this post, we will go over the story behind the maximum likelihood.