The application of Monte Carlo methods for learning generalized linear model

Abstract

Monte Carlo method is a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other mathematical methods. Basically, many statisticians have been increasingly drawn to Monte Carlo method in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. In this paper, we will introduce the Monte Carlo method for calculating coefficients in Generalized Linear Model(GLM), especially for Logistic Regression. Our main methods are Metropolis Hastings(MH) Algorithms and Stochastic Approximation in Monte Carlo Computation(SAMC). For comparison, we also get results automatically using MLE method in R software.