fabMix (version 5.1)

update_SigmaINV_xUC: Gibbs sampling for \(\Sigma^{-1}\) per component for xUC models

Description

Gibbs sampling for \(\Sigma^{-1}\) per component for xUC models

Usage

update_SigmaINV_xUC(x_data, z, y, Lambda, mu, K, alpha_sigma, beta_sigma)

Value

\(K\times p\times p\) array containing the inverse variance of errors per component under the restriction: \(\Sigma^{-1}_k = \sigma_k I_p\), where \(\sigma_k > 0\).

Arguments

x_data

\(n\times p\) matrix containing the observed data

z

Allocation vector

y

\(n\times q\) matrix containing the latent factors

Lambda

\(K\times p\times q\) array with factor loadings

mu

\(K\times p\) array containing the marginal means

K

Number of components

alpha_sigma

Prior parameter \(alpha\)

beta_sigma

Prior parameter \(beta\)

Author

Panagiotis Papastamoulis

Examples

library('fabMix')
# simulate some data
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)

# use the real values as input and update SigmaINV
update_SigmaINV_xUC(x_data = syntheticDataset$data, 
	z = syntheticDataset$class, 
	y = syntheticDataset$factors, 
	Lambda = syntheticDataset$factorLoadings, 
	mu = syntheticDataset$means, 
	K = K, 
	alpha_sigma = 0.5, beta_sigma = 0.5)