Introduction 日本語 ver Today, I will explain MAP estimation(maximum a posteriori estimation). MAP estimation is used Bayes' thorem. If sample data is few, we can not belive value by Maximum likelihood estimation. Then, MAP estimation is enable to include our sense. Overveiw Bayes' theorem MAP estimation Conjugate distribution Bayes' theorem Bayes' theorem is P(A|B) = \frac{P(B|A)P(A)}{P(B)}
P(A|B) is Probability when B occur. Please go on http://takutori.blogspot.com/2018/04/bayes-theorem.html to know detail of Bayes' theorem. Map estimation Map estimation is used Bayes' theorem. Map estimation estimate parameter of population by maximuzing posterior probability. Now, suppoce we get data x_1,x_2,...,x_n from population which have parameter \theta. Then, we want to P(\theta|x_1,x_2,...,x_n). Here, we use Bayes' theorem. $$P(\theta|x_1,x_2,...,x_n) = \frac{P(x_1,x_2,...,x_n | \theta ) P(\theta)}{P(x_1,x_2,...,x_n)}...