Variational Bayesian Method: Ritz Method in Stochastic System

Bayesian inference is to find posterior probabilities, but since it is difficult to find analytical solutions, it is often the case that approximate solutions are found. The variational Bayesian method is a powerful method for finding an approximate solution. It is a variational method in a stochastic system. Variational methods have been developed for the deterministic system since old times, and are one of the most powerful foundations for numerical solutions of a wide range of problems defined by partial differential equations. A detailed comparison and explanation of the classical variational principle and the variational Bayesian method are given, and the basic application examples of the variational Bayesian method are also given. Programming codes written in C are also shown to aid the readers’ understanding.