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cPseudoMaRg

An implementation of the Correlated Pseudo-Marginal Sampler.

Install

Install from CRAN by typing

install.packages("cPseudoMaRg")

in an R console. Alternatively, install from Github by typing

devtools::install_github("tbrown122387/cpm")

Example

Another Random Effects Model that mimics the example in the above paper. They estimate a mean parameter, whereas the unknown parameters here are variance parameters. Also, this model’s likelihood is nonidentifiable.

# y | x, theta ~ Normal(x, SSy)
# x | theta ~ Normal(0, SSx)
# theta = (SSy + SSx, SS_x)
# p(theta | y) propto p(y | theta)p(theta)
# approx p(y | theta) with mean( p(y | xi, theta)  ) where xi ~ p(xi | theta)

# real data
realxVar <- .2
realyVar <- .3
realTheta1 <- realxVar + realyVar
realTheta2 <- realxVar
realParams <- c(realTheta1, realTheta2)
numObs <- 10
realX <- rnorm(numObs, mean = 0, sd = sqrt(realxVar))
realY <- rnorm(numObs, mean = realX, sd = sqrt(realyVar))

# tuning params
numImportanceSamps <- 1000
numMCMCIters <- 10000
randomWalkScale <- 1.5
recordEveryTh <- 1
myLLApproxEval <- function(y, thetaProposal, uProposal){
  if( (thetaProposal[1] > thetaProposal[2]) & (all(thetaProposal > 0))){
    xSamps <- uProposal*sqrt(thetaProposal[2])
    logCondLikes <- sapply(xSamps,
                           function(xsamp) {
                             sum(dnorm(y,
                                       xsamp,
                                       sqrt(thetaProposal[1] - thetaProposal[2]),
                                       log = T)) })
    m <- max(logCondLikes)
    log(sum(exp(logCondLikes - m))) + m - log(length(y))
  }else{
    -Inf
  }
}
sampler <- makeCPMSampler(
  paramKernSamp = function(params){
    return(params + rnorm(2)*randomWalkScale)
  },
  logParamKernEval = function(oldTheta, newTheta){
    dnorm(newTheta[1], oldTheta[1], sd = randomWalkScale, log = TRUE)
         + dnorm(newTheta[2], oldTheta[2], sd = randomWalkScale, log = TRUE)
  },
  logPriorEval = function(theta){
    if( (theta[1] > theta[2]) & all(theta > 0)){
      0
    }else{
      -Inf
    }
  },
  logLikeApproxEval = myLLApproxEval,
  realY, numImportanceSamps, numMCMCIters, .99, recordEveryTh
)
res <- sampler(realParams)

# look at output
print(res)
plot(res)

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.