MixMVN_MCMC {MVNBayesian}

MCMC simulation for MVN mixture distribution

Description

Function to get a MCMC simulation results based on the imported MVN mixture distribution. It is commonly used for inquiring the specified conditional probability of MVN mixture distribuiton calculated through Bayesian posteriori.

Usage

# Bayesian posteriori mix MVN as input data:
# data <- MixMVN_BayesianPosteriori(dataset2[,1:4], 3)

# run MCMC simulation based on Bayesian posteriori mix MVN:
MixMVN_MCMC(data, steps, pars, values, tol, random_method, ...)

Arguments

data

A matrix-like data containing the mixture probability, mean vector and covariance matrix for each cluster in each row.

steps

A positive integer. The numbers of random vectors to be generated for MCMC step.

pars

A integer vector to declare fixed dimension(s). For example if the desired dimensions are 1st=7 and 3rd=10, set this argument as c(1,3).

values

A numeric vector to assign value(s) to declared dimension(s). For example if the desired dimensions are 1st=7 and 3rd=10, set this argument as c(7,10).

tol

Tolerance. A numeric value to control the generated vectors to be accepted or rejected. Criterion uses Euclidean distance in declared dimension(s). Default value is 0.3.

random_method

The method to generate random vectors. Options are "Gibbs": Gibbs sampling for MVN mixture model; and "Fast": call rmvnorm() to generate random vectors based on matrix factorization. Default option is "Fast".

...

Other arguments to control the process in Gibbs sampling if the random_method is "Gibbs".

Value

return a list which contains:

AcceptRate

Acceptance of declared conditions of MCMC

MCMCdata

All generated random vectors in MCMC step based on MVN mixture distribution

Accept

Subset of accepted sampling in MCMCdata

Reject

Subset of rejected sampling in MCMCdata

See Also

MixMVN_BayesianPosteriori, MixMVN_GibbsSampler, MVN_GibbsSampler, MVN_FConditional

Examples

library(plyr)
library(mvtnorm)
library(stats)

# dataset2 has 4 parameters: dimen1, dimen2, dimen3 and dimen4:
head(dataset2)
dataset2_dim <- dataset2[,1:4] # extract parametric columns

# Get posteriori parameters of dataset2 using kmeans 3 clustering:
MixBPos <- MixMVN_BayesianPosteriori(dataset2_dim, 3)

# If we want to know when dimen1=1, which clusters are accepted, run:
MixBPos_MCMC <- MixMVN_MCMC(MixBPos, steps=5000, pars=c(1), values=c(1), tol=0.3)
MixBPos_MCMC$AcceptRate
result <- MixBPos_MCMC$MCMCdata
head(result)

# count accepted samples by clustering:
count(result[which(result[,7]==1),5])

library(rgl)
# Visualization using plot3d() if necessary:
# Clustering result in the rest 3 dimensions:
plot3d(result[,2], result[,3], z=result[,4], col=result[,5], size=2)

# Acceptance rejection visualization:
plot3d(result[,2], result[,3], z=result[,4], col=result[,7]+1, size=2)