gibbs_mala_sampler {multinomialLogitMix}

The core of the Hybrid Gibbs/MALA MCMC sampler for the multinomial logit mixture.

Description

This function implements Gibbs sampling to update the mixing proportions and latent allocations variables of the mixture model. The coefficients of the logit model are updated according to Metropolis-Hastings type move, based on a Metropolis adjusted Langevin (MALA) proposal.

Usage

gibbs_mala_sampler(y, X, tau = 3e-05, nu2, K, mcmc_iter = 100, 
	alpha_prior = NULL, start_values = "EM", em_iter = 10, 
	thin = 10, verbose = FALSE, checkAR = NULL, 
	probsSave = FALSE, ar_low = 0.4, ar_up = 0.6)

Arguments

y

matrix of counts.

X

design matrix (including constant term).

tau

the variance of the normal prior distribution of the logit coefficients.

nu2

scale of the MALA proposal (positive).

K

number of components of the (overfitting) mixture model.

mcmc_iter

Number of MCMC iterations.

alpha_prior

Parameter of the Dirichlet prior distribution for the mixing proportions.

start_values

Optional list of starting values. Random initialization is used if this is not provided.

em_iter

Maximum number of iterations if an EM initialization is enabled.

thin

optional thinning of the generated MCMC output.

verbose

Boolean.

checkAR

Number of iterations to adjust the scale of the proposal in MALA mechanism during the initial warm-up phase of the sampler.

probsSave

Optional.

ar_low

Lowest threshold for the acceptance rate of the MALA proposal (optional) .

ar_up

Highest threshold for the acceptance rate of the MALA proposal (optional).

Value

nClusters

sampled values of the number of clusters (non-empty mixture components).

allocations

sampled values of the latent allocation variables.

logLikelihood

Log-likelihood values per MCMC iteration.

mixing_proportions

sampled values of mixing proportions.

coefficients

sapled values of the coefficients of the multinomial logit.

complete_logLikelihood

Complete log-likelihood values per MCMC iteration.

class_probs

Classification probabilities per iteration (optional).

AR

Acceptance rate of the MALA proposal.

Note

This function is used inside the prior tempering scheme, which is the main function.

Author(s)

Panagiotis Papastamoulis

See Also

gibbs_mala_sampler_ppt

Examples

#	Generate synthetic data
	K <- 2
	p <- 2
	D <- 2
	n <- 2
	set.seed(116)
	simData <- simulate_multinomial_data(K = K, p = p, D = D, n = n, size = 20, prob = 0.025)   


	gs <- gibbs_mala_sampler(y = simData$count_data, X = simData$design_matrix, 
		tau = 0.00035, nu2 = 100, K = 2, mcmc_iter = 3, 
		alpha_prior = rep(1,K), start_values = "RANDOM", 
		thin = 1, verbose = FALSE, checkAR = 100)