README.md

In wzh96/STAT600RPackage: Implementing Metropolis-Hastings Algorithm

STAT600RPackage

The Metropolis-Hastings algorithm is a powerful Markov chain method to simulate samples from probability distributions from which direct sampling is difficult. The detailed description of this algorithm can be found at (Chib and Greenberg, 1995).

The intented use of this package:

This package implements the Metropolis-Hastings Algorithm to simulate a sequence of random samples from a user defined probability distribution. This distribution can be any distribution defined by the user as a function. And the distribution can be either one dimensional or multi-dimensional. The user defined distribution serves as an input of the R package. For one dimensional distribution, the Gaussian distribution will be used as the candidate-generating density and for muti-dimensional distribution, mutivariate normal distribution will be used as the candidate-generating density. The user can define the standard deviation of the Gaussian distribution. The user can also define the number of iterations of the algorithm. After the sampling process, the R package will also be able to generate a histogram of the distribution.

Reference

Chib, S., Greenberg, E., 1995. Understanding the Metropolis-Hastings Algorithm. The American Statistician 49, 327–335. https://doi.org/10.1080/00031305.1995.10476177

Example of implementation

Multivariate Distribution (Multivariate Normal)

targetdensity <- function(x){ p <- length(x) mu <- c(4,-7,3,2,1) sigma <- sigma <- diag(1, p) d <- exp(-0.5 * t(x - mu) %*% solve(sigma) %*% (x - mu)) / ((2*pi)^(p/2) * sqrt(det(sigma))) return(d) }

sample <- MHAlogrithmmulti(targetdensity, nvar = 5, CGDensity = "multivariateNormal", niter = 1000)

Univariate Distribution (Exponential)

targetdensity = function(x){ d <- dexp(x, rate =1) return(d) }

sample <- MHAlogrithmuni(target, xinit = 0, sigma = 1, niter = 5000)

See Example.R for detail

wzh96/STAT600RPackage documentation built on Dec. 23, 2021, 6:15 p.m.