compute_A_B_G_D_and_simulate_mu_Lambda_CUU: Computation and simulations for CUU

In fabMix: Overfitting Bayesian Mixtures of Factor Analyzers with Parsimonious Covariance and Unknown Number of Components

Computation and simulations for CUU

Description

This function simulates \mu and \Lambda for the CUU model.

Usage

	compute_A_B_G_D_and_simulate_mu_Lambda_CUU(SigmaINV, 
		suff_statistics, OmegaINV, K, priorConst1, T_INV, v_r)

Arguments

SigmaINV	Precision matrix \Sigma^{-1}
suff_statistics	Sufficient statistics
OmegaINV	Prior parameter: \Omega^{-1}
K	Number of overfitting mixture components
priorConst1	Prior constant: T^{-1}\xi
T_INV	Prior parameter: T^{-1}\xi
v_r	This vector is used to set to zero the upper right (q-1)\times(q-1) diagonal block of factor loadings for identifiability purposes.

Value

A list containing a draw from the conditional distributions of \mu and \Lambda:

Lambdas	K\times p\times q array (factor loadings per component)
mu	K\times p array (marginal mean per component)

Author(s)

Panagiotis Papastamoulis

Examples

	library('fabMix')
	data(waveDataset1500)
	x_data <- scale(as.matrix(waveDataset1500[ 1:20, -1])) # data
	z <-  waveDataset1500[ 1:20, 1] # class
	p <- dim(x_data)[2]
	n <- dim(x_data)[1]
	q <- 2
	K <- length(table(z))           # 3 classes
	# give some arbitrary values to the parameters:
	set.seed(1)
	mu <- array( runif(K * p), dim = c(K,p) )
	y <- array(rnorm(n = q*n), dim = c(n,q))
	SigmaINV <- array(data = 0, dim = c(K,p,p) )
	for(k in 1:K){
		diag(SigmaINV[k,,]) <- 0.5 + 0.5*runif(p)
	}
	OmegaINV <- diag(q)
	# compute sufficient stats 
	suf_stat <- compute_sufficient_statistics_given_mu(y = y, 
	 z = z, K = K, x_data = x_data, mu = mu)

	v_r <- numeric(p) #indicates the non-zero values of Lambdas
	for( r in 1:p ){
		v_r[r] <- min(r,q)
	}
	T_INV <- array(data = 0, dim = c(p,p))
	diag(T_INV) <- diag(var(x_data))
	diag(T_INV) <- 1/diag(T_INV)
	ksi <- colMeans(x_data)
	priorConst1 <- array(diag(T_INV)*ksi, dim =c(p,1))
	# now simulate mu and Lambda
	f2 <- compute_A_B_G_D_and_simulate_mu_Lambda_CUU(SigmaINV = SigmaINV, 
                suff_statistics = suf_stat, OmegaINV = OmegaINV, 
                K = K, priorConst1 = priorConst1, T_INV = T_INV, v_r = v_r)
	# f2$mu contains the simulated means
	# f2$Lambdas contains the simulated factor loadings

fabMix documentation built on May 29, 2024, 2:53 a.m.