consensusMCcov {parallelMCMCcombine}

Consensus Monte Carlo Algorithm (for correlated parameters)

Description

The function uses the Consensus Monte Carlo algorithm introduced by Scott et al. (see References) to combine the independent subset posterior samples subchains into the set of samples that estimate the posterior density given the full data set. The Consensus Monte Carlo algorithm uses a weighted average of the subset posterior samples to produce the combined posterior samples, where the weights are based on the inverse variance-covariance matrix of the subset posterior samples.

Usage

consensusMCcov(subchain, shuff = FALSE)

Arguments

subchain

array of subset posterior samples of the dimension c(d,sampT,M). Here d is the dimension of the parameter space, sampT is the number of samples, and M is the number of subposterior datasets.

shuff

shuff: logical; if TRUE, each of the M subsets of d dimensional parameters in subchain is shuffled.

Details

The array subchain must have dimension c(d,sampT,M). Here d is the dimension of the parameter space, sampT is the number of samples, and M is the number of subposterior datasets.

Value

Returns an array of samples of dimension dim=c(d,sampT) representing an estimated (combined) full posterior density.

References

Scott, S.L., Blocker, A. W., Bonassi (2013) Bayes and Big Data: The consensus Monte Carlo Algorithm. Bayes 250.

Examples

d      <- 2     # dimension of the parameter space  
sampT  <- 1000  # number of subset posterior samples
M      <- 3     # total number of subsets

## simulate Gaussian subposterior samples

theta <- array(NA,c(d,sampT,M)) 

norm.mean <- c(1.0, 2.0)
norm.sd   <- c(0.5, 1.0)

for (i in 1:d)
  for (s in 1:M)        
    theta[i,,s] <- rnorm(sampT, mean=norm.mean[i]+runif(1,-0.01,0.01), sd=norm.sd[i])

## combine samples:

full.theta <- consensusMCcov(subchain=theta, shuff=FALSE)