gibbs_mala_sampler_ppt {multinomialLogitMix}

Prior parallel tempering scheme of hybrid Gibbs/MALA MCMC samplers for the multinomial logit mixture.

Description

The main MCMC scheme of the package. Multiple chains are run in parallel and swaps between are proposed. Each chain uses different parameters on the Dirichlet prior of the mixing proportion. The smaller concentration parameter should correspond to the first chain, which is the one that used for inference. Subsequent chains should have larger values of concentration parameter for the Dirichlet prior.

Usage

gibbs_mala_sampler_ppt(y, X, tau = 3e-05, nu2, K, 
	mcmc_cycles = 100, iter_per_cycle = 10, dirPriorAlphas, 
	start_values = "EM", em_iter = 10, nChains = 4, nCores = 4, 
	warm_up = 100, checkAR = 50, probsSave = FALSE, 
	showGraph = 50, ar_low = 0.4, ar_up = 0.6, withRandom = TRUE)

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_cycles

Number of MCMC cycles. At the end of each cycle, a swap between chains is attempted.

iter_per_cycle

Number of iterations per cycle.

dirPriorAlphas

Vector of concentration parameters for the Dirichlet priors in increasing order.

start_values

Optional list of start values. Randomly generated values are used if this is not provided.

em_iter

Maximum number of iterations if an EM initialization is enabled.

nChains

Total number of parallel chains.

nCores

Total number of CPU cores for parallel processing of the nChains.

warm_up

Initial warm-up period of the sampler, in order to adaptively tune the scale of the MALA proposal (optional).

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.

showGraph

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).

withRandom

Logical. If TRUE (default) then a random permutation is applied to the supplied starting values.

Details

See the paper for details.

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

The output of the MCMC sampler is not identifiable, due to possible label switching. In order to draw meaningful inferences, the output should be post-processed by dealWithLabelSwitching.

Author(s)

Panagiotis Papastamoulis

References

Papastamoulis, P (2022). Model-based clustering of multinomial count data.

Examples

#	Generate synthetic data

	K <- 2
	p <- 2
	D <- 3
	n <- 2
	set.seed(116)
	simData <- simulate_multinomial_data(K = K, p = p, D = D, n = n, size = 20, prob = 0.025)   



# apply mcmc sampler based on random starting values 

Kmax = 2
nChains = 2
dirPriorAlphas  = c(1, 1 + 5*exp((seq(2, 14, length = nChains - 1)))/100)/(200)
nCores <- 2
mcmc_cycles <- 2
iter_per_cycle = 2
warm_up <- 2

mcmc_random1 <-  gibbs_mala_sampler_ppt( y = simData$count_data, X = simData$design_matrix, 
		tau = 0.00035, nu2 = 100,  K = Kmax, dirPriorAlphas = dirPriorAlphas,
		mcmc_cycles = mcmc_cycles, iter_per_cycle = iter_per_cycle, 
		start_values = 'RANDOM', 
		nChains = nChains, nCores = nCores, warm_up = warm_up, showGraph = 1000, 
		checkAR = 1000)

#sampled values for the number of clusters (non-empty mixture components) per chain (columns)
mcmc_random1$nClusters