fabMix (version 5.1)

update_all_y_Sj: Gibbs sampling for \(y\) in xUx model

Description

Gibbs sampling for updating the factors \(y\) for models with different variance of errors per component.

Usage

update_all_y_Sj(x_data, mu, SigmaINV, Lambda, z)

Value

A matrix with generated factors

Arguments

x_data

\(n\times p\) matrix with obseved data

mu

\(n\times p\) matrix of marginal means

SigmaINV

\(K\times p\times p\) array containing the precision matrix per component

Lambda

\(p\times q\) matrix of factor loadings

z

Allocation vector

Author

Panagiotis Papastamoulis

Examples

library('fabMix')

n = 8                # sample size
p = 5                # number of variables
q = 2                # number of factors
K = 2                # true number of clusters

sINV_diag = 1/((1:p))    # diagonal of inverse variance of errors
set.seed(100)
syntheticDataset <- simData(sameLambda=TRUE,K.true = K, n = n, q = q, p = p, 
                        sINV_values = sINV_diag)
# add some noise here:
SigmaINV <- array(data = 0, dim = c(K,p,p))
for(k in 1:K){
        diag(SigmaINV[k,,]) <- 1/diag(syntheticDataset$variance) + rgamma(p, shape=1, rate = 1)
}

# use the real values as input and simulate factors
update_all_y_Sj(x_data = syntheticDataset$data, 
		mu = syntheticDataset$means, 
		SigmaINV = SigmaINV, 
		Lambda = syntheticDataset$factorLoadings, 
		z = syntheticDataset$class)