AntMAN {AntMAN}

AntMAN: A package for fitting finite Bayesian Mixture models with a random number of components

Description

AntMAN: Anthology of Mixture ANalysis tools AntMan is an R package fitting Finite Bayesian Mixture models with a random number of components. The MCMC algorithm behind AntMAN is based on point processes and offers a more computationally efficient alternative to the Reversible Jump. Different mixture kernels can be specified: univariate Gaussian, multivariate Gaussian, univariate Poisson, and multivariate Bernoulli (Latent Class Analysis). For the parameters characterising the mixture kernel, we specify conjugate priors, with possibly user specified hyper-parameters. We allow for different choices on the prior on the number of components: Shifted Poisson, Negative Binomial, and Point Masses (i.e. mixtures with fixed number of components).

Package Philosophy

The main function of the AntMAN package is AM_mcmc_fit. AntMAN performs a Gibbs sampling in order to fit, in a Bayesian framework, a mixture model of a predefined type mix_kernel_hyperparams given a sample y. Additionally AntMAN allows the user to specify a prior on the number of components mix_components_prior and on the weights mix_weight_prior of the mixture. MCMC parameters mcmc_parameters need to be given as argument for the Gibbs sampler (number of interations, burn-in, ...). Initial values for the number of clusters (init_K) or a specific clustering allocation (init_clustering) can also be user-specified. Otherwise, by default, we initialise each element of the sample y to a different cluster allocation. This choice can be computationally inefficient.

For example, in order to identify clusters over a population of patients given a set of medical assumptions:

mcmc = AM_mcmc_parameters(niter=20000) 
mix = AM_mix_hyperparams_multiber () 
fit = AM_mcmc_fit (mix, mcmc) 
summary (fit)

In this example AM_mix_hyperparams_multiber is one of the possible mixtures to use.

AntMAN currently support four different mixtures :

AM_mix_hyperparams_unipois(alpha0, beta0) 
AM_mix_hyperparams_uninorm(m0, k0, nu0, sig02) 
AM_mix_hyperparams_multiber(a0, b0) 
AM_mix_hyperparams_multinorm(mu0, ka0, nu0, Lam0)

Additionally, three types of kernels on the prior number of components are available:

AM_mix_components_prior_pois()
AM_mix_components_prior_negbin() 
AM_mix_components_prior_dirac()

For example, in the context of image segmentation, if we know that there are 10 colours present, a prior dirac can be used :

mcmc = AM_mcmc_parameters(niter=20000) 
mix = AM_mix_hyperparams_multinorm () 
prior_component = AM_mix_components_prior_dirac(10) #  10 colours present
fit = AM_mcmc_fit (mix, prior_component, mcmc) 
summary (fit)