randomWalkMetropolis {EMC}R Documentation

The Random Walk Metropolis algorithm

Description

Given a target density function and a symmetric proposal generating function, this function produces samples from the target using the random walk Metropolis algorithm.

Usage

randomWalkMetropolis(nIters,              
                     startingVal,         
                     logTarDensFunc,      
                     propNewFunc,         
                     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.
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 and propNewFunc.

Details

propNewFunc
The propNewFunc is called multiple times by varying the block argument over 1:length(MHBlocks), so this function should know how to generate a proposal from the currentDraw 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

MetropolisHastings, parallelTempering, evolMonteCarlo

Examples

samplerObj <-
    with(CigarShapedFuncGenerator1(-13579),
         randomWalkMetropolis(nIters         = 5000,
                              startingVal    = c(0, 0),
                              logTarDensFunc = logTarDensFunc,
                              propNewFunc    = propNewFunc,
                              verboseLevel   = 1))
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]