MetropolisHastings {EMC}R Documentation

The Metropolis-Hastings algorithm

Description

Given a target density function and an asymmetric proposal distribution, this function produces samples from the target using the Metropolis Hastings algorithm.

Usage

MetropolisHastings(nIters,
                   startingVal,         
                   logTarDensFunc,      
                   propNewFunc,         
                   logPropDensFunc,     
                   MHBlocks      = NULL,
                   MHBlockNTimes = NULL,
                   saveFitness   = FALSE, 
                   verboseLevel  = 0,
                   ...)    

Arguments

Below sampDim refers to the dimension of the sample space.

nIters integer > 0.
startingVal double vector of length sampDim.
logTarDensFunc function of two arguments (draw, ...) that returns the target density evaluated in the log scale.
propNewFunc function of three arguments (block, currentDraw, ...) that returns new Metropolis-Hastings proposals. See details below on the argument block.
logPropDensFunc function of four arguments (block, currentDraw, proposalDraw, ...) that returns the proposal density evaluated in the log scale. See details below on the argument block.
MHBlocks list of integer vectors giving dimensions to be blocked together for sampling. It defaults to as.list(1:sampDim), i.e., each dimension is treated as a block on its own. See details below for an example.
MHBlockNTimes integer vector of number of times each block given by MHBlocks should be sampled in each iteration. It defaults to rep(1, length(MHBlocks)). See details below for an example.
saveFitness logical indicating whether fitness values should be saved. See details below.
verboseLevel integer, a value >= 2 produces a lot of output.
... optional arguments to be passed to logTarDensFunc, propNewFunc and logPropDensFunc.

Details

propNewFunc and logPropDensFunc
The propNewFunc and the logPropDensFunc are called multiple times by varying the block argument over 1:length(MHBlocks), so these functions should know how to generate a proposal from the currentDraw or to evaluate the proposal density depending on which block was passed as the argument. See the example section for sample code.
MHBlocks and MHBlockNTimes
Blocking is an important and useful tool in MCMC that helps speed up sampling and hence mixing. Example: Let sampDim = 6. Let we want to sample dimensions 1, 2, 4 as one block, dimensions 3 and 5 as another and treat dimension 6 as the third block. Suppose we want to sample the three blocks mentioned above 1, 5 and 10 times in each iteration, respectively. Then we could set MHBlocks = list(c(1, 2, 4), c(3, 5), 6) and MHBlockNTimes = c(1, 5, 10)
saveFitness
The term fitness refers to the negative of the logTarDensFunc values. By default, the fitness values are not saved, but one can do so by setting saveFitness = TRUE.

Value

This function returns a list with the following components:

draws matrix of dimension nIters x sampDim, if saveFitness = FALSE. If saveFitness = TRUE, then the returned matrix is of dimension nIters x (sampDim + 1), where the fitness values appear in its last column.
acceptRatios matrix of the acceptance rates.
detailedAcceptRatios matrix with detailed summary of the acceptance rates.
nIters the nIters argument.
startingVal the startingVal argument.
time the time taken by the run.

Note

The effect of leaving the default value NULL for some of the arguments above are as follows:

MHBlocks as.list(1:sampDim).

MHBlockNTimes

rep(1, length(MHBlocks)).

Author(s)

Gopi Goswami goswami@stat.harvard.edu

References

Jun S. Liu (2001). Monte Carlo strategies for scientific computing. Springer.

See Also

randomWalkMetropolis, parallelTempering, evolMonteCarlo

Examples

samplerObj <-
    with(CigarShapedFuncGenerator2(-13579),
         MetropolisHastings(nIters          = 5000,
                            startingVal     = c(0, 0),
                            logTarDensFunc  = logTarDensFunc,
                            propNewFunc     = propNewFunc,
                            logPropDensFunc = logPropDensFunc,
                            verboseLevel    = 2))
print(samplerObj)
print(names(samplerObj))
with(samplerObj,
 {
     print(detailedAcceptRatios)
     print(dim(draws))
     plot(draws,
          xlim = c(-3, 5),
          ylim = c(-3, 4),
          pch  = '.',
          ask  = FALSE,
          main = as.expression(paste('# draws:', nIters)),
          xlab = as.expression(substitute(x[xii], list(xii = 1))),
          ylab = as.expression(substitute(x[xii], list(xii = 2))))    
 })

[Package EMC version 1.1 Index]