MixMVN_GibbsSampler {MVNBayesian}

Gibbs sampler for MVN mixture distribution

Description

Generating random vectors on the basis of a given MVN mixture distribution, through Gibbs sampling algorithm or matrix factorization.

Usage

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

# Generate random vectors based on Bayesian posteriori MVN mixture:
MixMVN_GibbsSampler(n, data, random_method = c("Gibbs", "Fast"), reject_rate=0, ...)

Arguments

n

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

data

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

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.

reject_rate

A numeric value which will be efficient if the random_method is "Gibbs": Determine the discarded items in burn-in period by ratio. Default value is 0. For details see MVN_GibbsSampler.

...

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

Details

It is recommanded using the random method of "Fast" due to the high efficiency. The time complexity of "Gibbs" method is O(k*n) where the k means dimensionality of MVN mixture model and n means generated numbers of random vectors; while that of the "Fast" method is only O(n), without considering the effect of burn-in period. this discrepancy will be even further significant when we use MCMC methods to do some further analysis in which random vectors will be generated every time when we set conditions.

Value

return a series random vectors in the basis of given MVN mixture distribution.

See Also

Ascending_Num, MixMVN_BayesianPosteriori, MVN_BayesianPosteriori

Examples

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

# Use dataset2 for demonstration. Get parameters of Bayesian
# posteriori multivariate normal mixture distribution
head(dataset2)
dataset2_par <- dataset2[,1:4] # only parameter columns are premitted
MixBPos <- MixMVN_BayesianPosteriori(dataset2_par, species=3)
MixBPos

# Generate random vectors using Gibbs sampling:
MixBPos_Gibbs <- MixMVN_GibbsSampler(5000, MixBPos, random_method = "Gibbs")
head(MixBPos_Gibbs)

# Compared generation speed of "Gibbs" to that of "Fast"
MixBPos_Fast <- MixMVN_GibbsSampler(5000, MixBPos, random_method = "Fast")
head(MixBPos_Fast)

# Visulization by clusters:
library(rgl)
dimen1 <- MixBPos_Gibbs[,1]
dimen2 <- MixBPos_Gibbs[,2]
dimen3 <- MixBPos_Gibbs[,3]
dimen4 <- MixBPos_Gibbs[,4]
plot3d(x=dimen1, y=dimen2, z=dimen3, col=MixBPos_Gibbs[,5], size=2)