[Review] MLE and MAP ~Maximum Likelihood Estimate and Maximum a Posteriori Probatility~

Introduction

This article aims at explaining the whole picture of MLE and MAP, then makes the difference between them clear.

Agenda

1. MLE
2. MAP

MLE

In statics, MLE is a method of estimating the parameters of a statistical model, given observations. MLE attempts to find the parameter values that maximise the likelihood function, given the observations. The resulting estimate is called a maximum likelihood estimate.

The methods of ML(maximum likelihood) is used with a wide range of statistical analyses. As an example, let's say that we are interested in the heights of adult female penguins, but are unable to measure the height of every penguin in a population. Assuming that the heights are normally distributed with some unknown mean and variance, the mean and variance can be estimated with MLE while only knowing the heights of some sample of the overall population. MLE would accomplish that by taking the mean and variance as parameters and finding particular parametric values that make the observed results the most probable given the normal model.