# MVNBayesian-package: Bayesian Analysis Framework for MVN (Mixture) Distribution In CubicZebra/MVNBayesian: Bayesian Analysis Framework for MVN (Mixture) Distribution

## Description

Tools of Bayesian analysis framework using the method suggested by Berger (1985) <doi:10.1007/978-1-4757-4286-2> for multivariate normal (MVN) distribution and multivariate normal mixture (MixMVN) distribution: a) calculating Bayesian posteriori of (Mix)MVN distribution; b) generating random vectors of (Mix)MVN distribution; c) Markov chain Monte Carlo (MCMC) for (Mix)MVN distribution.

## Details

This package is aimed to build a easy approach for MVN (mixture) distribution in Bayesian analysis framework. Bayesian posteriori MVN (mixture) distribution can be calculated in conditions of given priori MVN (mixture) informations. The conjugated property of MVN distribution makes it effective in parameter estimation using Bayesian iterator. Joint and marginal probability densities of a certain MVN (mixture) can be achieved through random vector generator, using Gibbs sampling. Conditional probability densities from a certain MVN (mixture) can be simulated using MCMC method.

## Author(s)

ZHANG Chen

Maintainer: ZHANG Chen <447974102@qq.com>

## References

"Statistical Inference" by George Casella. Roger L. Berger;
"Statistical Decision Theory and Bayesian Analysis" by James O. Berger;
"Matrix Computation" by Gee H. Golub. Charles F. Van Loan;
"Bayesian Statistics" by WEI Laisheng;
"Machine Learning" by NAKAGAWA Hiroshi.

`stats`, `mvtnorm`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```library(Rfast) library(mvtnorm) library(plyr) head(dataset1) BP <- MVN_BayesianPosteriori(dataset1) BP BP_Gibbs <- MVN_GibbsSampler(5000, BP) colMeans(BP_Gibbs) colrange(BP_Gibbs) result <- MVN_MCMC(BP, 5000, c(1), c(77.03)) result\$Accept ```