AM_mcmc_fit: Performs a Gibbs sampling
In AntMAN: Anthology of Mixture Analysis Tools

Description Usage Arguments Details Value Examples

The AM_mcmc_fit function performs a Gibbs sampling in order to estimate the mixture comprising the sample data y. The mixture selected must be of a predefined type mix_kernel_hyperparams (defined with AM_mix_hyperparams_* functions, where star * denotes the chosen kernel). Additionally, a prior distribution on the number of mixture components must be specified through mix_components_prior (generated with AM_mix_components_prior_* functions, where * denotes the chosen prior). Similarly, a prior on the weights of the mixture should be specified through mix_weight_prior (defined with AM_mix_weights_prior_* functions). Finally, with mcmc_parameters, the user sets the MCMC parameters for the Gibbs sampler (defined with AM_mcmc_parameters functions).

AM_mcmc_fit(
  y,
  mix_kernel_hyperparams,
  initial_clustering = NULL,
  init_K = NULL,
  fixed_clustering = NULL,
  mix_components_prior = AM_mix_components_prior_pois(),
  mix_weight_prior = AM_mix_weights_prior_gamma(),
  mcmc_parameters = AM_mcmc_parameters()
)

`y`	input data, can be a vector or a matrix.
`mix_kernel_hyperparams`	is a configuration list, defined by _mix_hyperparams functions, where denotes the chosen kernel. See `AM_mix_hyperparams_multiber`, `AM_mix_hyperparams_multinorm`, `AM_mix_hyperparams_uninorm`, `AM_mix_hyperparams_unipois` for more details.
`initial_clustering`	is a vector CI of initial cluster assignement. If no clustering is specified (either as `init_K` or `init_clustering`), then every observation is assigned to its own cluster.
`init_K`	initial value for the number of cluster. When this is specified, AntMAN intitialises the clustering assign usng K-means.
`fixed_clustering`	if specified, this is the vector CI containing the cluster assignments. This will remain unchanged for every iteration.
`mix_components_prior`	is a configuration list defined by AM_mix_components_prior_* functions, where * denotes the chosen prior. See `AM_mix_components_prior_dirac`, `AM_mix_components_prior_negbin`, `AM_mix_components_prior_pois` for more details.
`mix_weight_prior`	is a configuration list defined by AM_weight_prior_* functions, where * denotes the chosen prior specification. See `AM_mix_weights_prior_gamma` for more details.
`mcmc_parameters`	is a configuration list defined by AM_mcmc_parameters. See `AM_mcmc_parameters` for more details.

If no initial clustering is specified (either as init_K or init_clustering), then every observation is allocated to a different cluster. If init_K is specified then AntMAN initialises the clustering through K-means.

Warning: if the user does not specify init_K or initial_cluster, the first steps can be be time-consuming because of default setting of the initial clustering.

The return value is an AM_mcmc_output object.

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 AM_mcmc_fit( AM_sample_unipois()$y, 
              AM_mix_hyperparams_unipois (alpha0=2, beta0=0.2), 
              mcmc_parameters = AM_mcmc_parameters(niter=50, burnin=0, thin=1, verbose=0))