simpleMergeSplit {sams}

Merge-Split Sampling for a Partition Using Uniformly Random Allocation

Description

Merge-split proposals for conjugate "Chinese Restaurant Process" (CRP) mixture models using uniformly random allocation of items, as presented in Jain & Neal (2004), with additional functionality for the two parameter CRP prior.

Usage

simpleMergeSplit(
  partition,
  logPosteriorPredictiveDensity = function(i, subset) 0,
  mass = 1,
  discount = 0,
  nUpdates = 1L,
  selectionWeights = NULL
)

Arguments

partition

A numeric vector of cluster labels representing the current partition.

logPosteriorPredictiveDensity

A function taking an index i (as a numeric vector of length one) and a subset of integers subset, and returning the natural logarithm of p( y_i | y_subset ), i.e., that item's contribution to the log integrated likelihood given a subset of the other items. The default value "turns off" the likelihood, resulting in prior simulation (rather than posterior simulation).

mass

A specification of the mass (concentration) parameter in the CRP prior. Must be greater than the -discount argument.

discount

A numeric value on the interval [0,1) corresponding to the discount parameter in the two parameter CRP prior.

nUpdates

An integer giving the number of merge-split proposals before returning. This has the effect of thinning the Markov chain.

selectionWeights

A matrix or data frame whose first two columns are the unique pairs of data indices, along with a column of weights representing how likely each pair is to be selected at the beginning of each merge-split update.

Value

partition

An integer vector giving the updated partition encoded using cluster labels.

accept

The acceptance rate of the Metropolis-Hastings proposals, i.e. the number accepted proposals divided by nUpdates.

References

Jain, S., & Neal, R. M. (2004). A split-merge Markov chain Monte Carlo procedure for the Dirichlet process mixture model. Journal of computational and Graphical Statistics, 13(1), 158-182.