shallot (version 0.4.1)

sample.partitions.posterior: Sample Partitions from Posterior Distribution of Partition

Description

This function samples partitions from the posterior distribution of a partition based on a user-supplied likelihood and the following prior partition distributions: Ewens, Ewens-Pitman, Ewens attraction, Ewens-Pitman attraction, and ddCRP distributions.

Usage

sample.partitions.posterior(partition, sampling.model, partition.model,
    n.draws, massRWSD = 0.5, discountRWSD = 0.1,
    k = min(length(partition), 25), temperatureRWSD = 0.5,
    progress.bar = interactive())

Arguments

partition

An object of class shallot.distribution.data

sampling.model

An object of class shallot.distribution.data obtained from the sampling.model function.

partition.model

An object of class shallot.distribution obtained, for example, from the ewens.pitman.attraction function.

n.draws

An integer representing the desired number of samples.

massRWSD

The standard deviation of the random walk proposal for updating the mass parameter.

discountRWSD

The standard deviation of the random walk proposal for updating the discount parameter.

k

The number of items to shuffle when proposing an update for the permutation.

temperatureRWSD

The standard deviation of the random walk proposal for updating the temperature parameter.

progress.bar

Should a progress bar be shown while sampling?

Value

An object of class shallot.samples.raw which can be subsequently be used in process.samples, pairwise.probabilities, estimate.partition,

See Also

partition.distribution, process.samples, pairwise.probabilities, estimate.partition sample.partitions

Examples

# NOT RUN {
mass <- mass(1.0, fixed=TRUE)
discount <- discount(0.05, fixed=TRUE)
distance <- dist(scale(USArrests[1:9,]))
if ( min(distance[upper.tri(distance)],na.rm=TRUE) == 0 )
  stop("Oops, distances must be strictly positive.")

n.items <- attr(distance,"Size")
permutation <- permutation(n.items=n.items, fixed=FALSE)
temperature <- temperature(2,fixed=TRUE)
attraction <- attraction(permutation,decay.exponential(temperature,distance))
partition.distribution <- ewens.pitman.attraction(mass, discount, attraction)

## Model inputs.
data <- c(-1.48, -1.40, -1.16, -1.08, -1.02, 0.14, 0.51, 0.53, 0.78)
sigma  <- 0.1
mu0    <- 0.0
sigma0 <- 1.0

## Derived values.
s2 <- sigma * sigma
s02 <- sigma0 * sigma0
s02Inv <- 1.0 / s02
c <- -1.0 / (2.0 * s2)

## Sampling model of Neal (JCGS, 2009)
## Function to perform an MCMC update of the parameter.
sample.parameter <- function(indices=c(), parameter=NULL) {
  sum <- sum(data[indices])
  variance <- 1 / (s02Inv + length(indices) / s2)
  mean <- variance * (mu0 / s02 + sum / s2)
  rnorm(1, mean=mean, sd=sqrt(variance))
}

## Function to evaluate the likelihood contribution for an observation.
log.density <- function(i, indices, parameter) {
  resid <- data[i] - parameter
  c * resid * resid
}

sampling.model <- sampling.model(sample.parameter, log.density)

## Perform posterior sampling.
initial.partition <- rep(1,length(data))
n.draws <- 100
raw <- sample.partitions.posterior(initial.partition,sampling.model,partition.distribution,
                                   massRWSD=3,temperatureRWSD=1,n.draws)
samples.format1 <- process.samples(raw,as.matrix=TRUE)
samples.format2 <- process.samples(raw,as.matrix=TRUE, expand=TRUE)
samples.format3 <- process.samples(raw,as.matrix=FALSE)

tail(samples.format1$hyperparameters)

## Shrinkage to group means?
plot(data,apply(samples.format2$partitions,2,mean))
abline(a=0,b=1)

## Post processing to find the partition estimate.
pp <- pairwise.probabilities(raw)
est <- estimate.partition(raw, pp)
plot(confidence(pp,est))

samples.format1$hyperparameters
# }