getSamplesDPmeasure: Get posterior samples for a Dirichlet process measure

In nimble: MCMC, Particle Filtering, and Programmable Hierarchical Modeling

Get posterior samples for a Dirichlet process measure

Description

This function obtains posterior samples from a Dirichlet process distributed random measure of a model specified using the dCRP distribution.

Usage

getSamplesDPmeasure(
  MCMC,
  epsilon = 1e-04,
  setSeed = FALSE,
  progressBar = getNimbleOption("MCMCprogressBar")
)

Arguments

MCMC	an MCMC class object, either compiled or uncompiled.
epsilon	used for determining the truncation level of the representation of the random measure.
setSeed	Logical or numeric argument. If a single numeric value is provided, R's random number seed will be set to this value. In the case of a logical value, if TRUE, then R's random number seed will be set to 1. Note that specifying the argument setSeed = 0 does not prevent setting the RNG seed, but rather sets the random number generation seed to 0. Default value is FALSE.
progressBar	Logical specifying whether to display a progress bar during execution (default = TRUE). The progress bar can be permanently disabled by setting the system option nimbleOptions(MCMCprogressBar = FALSE)

Details

This function provides samples from a random measure having a Dirichlet process prior. Realizations are almost surely discrete and represented by a (finite) stick-breaking representation (Sethuraman, 1994), whose atoms (or point masses) are independent and identically distributed. This sampler can only be used with models containing a dCRP distribution.

The MCMC argument is an object of class MCMC provided by buildMCMC, or its compiled version. The MCMC should already have been run, as getSamplesDPmeasure uses the posterior samples to generate samples of the random measure. Note that the monitors associated with that MCMC must include the cluster membership variable (which has the dCRP distribution), the cluster parameter variables, all variables directly determining the dCRP concentration parameter, and any stochastic parent variables of the cluster parameter variables. See help(configureMCMC) or help(addMonitors) for information on specifying monitors for an MCMC.

The epsilon argument is optional and used to determine the truncation level of the random measure. epsilon is the tail probability of the random measure, which together with posterior samples of the concentration parameter, determines the truncation level. The default value is 1e-4.

The output is a list of matrices. Each matrix represents a sample from the random measure. In order to reduce the output's dimensionality, the weights of identical atoms are added up. The stick-breaking weights are named weights and the atoms are named based on the cluster variables in the model.

For more details about sampling the random measure and determining its truncation level, see Section 3 in Gelfand, A.E. and Kottas, A. 2002.

Author(s)

Claudia Wehrhahn and Christopher Paciorek

References

Sethuraman, J. (1994). A constructive definition of Dirichlet priors. Statistica Sinica, 639-650.

Gelfand, A.E. and Kottas, A. (2002). A computational approach for full nonparametric Bayesian inference under Dirichlet process mixture models. Journal of Computational and Graphical Statistics, 11(2), 289-305.

See Also

buildMCMC, configureMCMC,

Examples

## Not run: 
  conf <- configureMCMC(model)
  mcmc <- buildMCMC(conf)
  cmodel <- compileNimble(model)
  cmcmc <- compileNimble(mcmc, project = model)
  runMCMC(cmcmc, niter = 1000)
  outputG <- getSamplesDPmeasure(cmcmc)

## End(Not run)

nimble documentation built on July 9, 2023, 5:24 p.m.