EMC (version 1.1)

findMaxTemper: Find the maximum temperature for parallel MCMC chains

Description

Multiple MCMC chains based algorithms (e.g., parallel tempering, evolutionary Monte Carlo) need a temperature ladder. This function finds the maximum temperature for constructing the ladder.

Usage

findMaxTemper(nIters,
              statsFuncList,
              startingVals,
              logTarDensFunc,
              MHPropNewFunc,
              logMHPropDensFunc = NULL, 
              temperLadder      = NULL,
              temperLimits      = NULL,
              ladderLen         = 10,
              scheme            = 'exponential',
              schemeParam       = 0.5,
              cutoffDStats      = 1.96,
              cutoffESS         = 50,
              guideMe           = TRUE,
              levelsSaveSampFor = NULL,
              saveFitness       = FALSE,
              doFullAnal        = TRUE,
              verboseLevel      = 0,
              ...)

Arguments

nIters

integer $>$ 0.

statsFuncList

list of functions of one argument each, which return the value of the statistic evaluated at one MCMC sample or draw.

startingVals

double matrix of dimension temperLadderLen $\times$ sampDim or vector of length sampDim, in which case the same starting values are used for every temperature level.

logTarDensFunc

function of two arguments (draw, ...) that returns the target density evaluated in the log scale.

MHPropNewFunc

function of four arguments (temperature, block, currentDraw, ...) that returns new Metropolis-Hastings proposals. See details below on the argument block.

logMHPropDensFunc

function of five arguments (temperature, block, currentDraw, proposalDraw, ...) that returns the proposal density evaluated in the log scale. See details below on the argument block.

temperLadder

double vector with all positive entries, in decreasing order.

temperLimits

double vector with two positive entries.

ladderLen

integer $>$ 0.

scheme

character.

schemeParam

double $>$ 0.

cutoffDStats

double $>$ 0.

cutoffESS

double $>$ 0.

guideMe

logical.

levelsSaveSampFor

integer vector with positive entries.

saveFitness

logical.

doFullAnal

logical.

verboseLevel

integer, a value $\ge$ 2 produces a lot of output.

...

optional arguments to be passed to logTarDensFunc, MHPropNewFunc and logMHPropDensFunc.

Value

• This function returns a list with the following components:
• temperLadder
  the temperature ladder used for the underlying MCMC run.
• DStats
  the D-statistic (Goswami and Liu, 2007) values used to find the maximum temperature.
• cutoffDStats
  the cutoffDStats argument.
• nIters
  the post burn-in nIters.
• levelsSaveSampFor
  the levelsSaveSampFor argument.
• draws
  array of dimension nIters $\times$ sampDim $\times$ levelsSaveSampForLen, if saveFitness = FALSE. If saveFitness = TRUE, then the returned array is of dimension nIters $\times$ (sampDim + 1) $\times$ levelsSaveSampForLen; i.e., each of the levelsSaveSampForLen matrices contain the fitness values in their last column.
• startingVals
  the startingVals argument.
• intermediate statistics
  a bunch of intermediate statistics used in the computation of DStats, namely, MCEsts, MCVarEsts, MCESS, ISEsts, ISVarEsts, ISESS, each being computed for all the statistics provided by statsFuncList argument.
• time
  the time taken by the run.

Details

This function is based on the method to find the temperature range introduced in section 4.1 of Goswami and Liu (2007).

[object Object],coord1 <- function (xx) { xx[1] }

coord3 <- function (xx) { xx[3] } statsFuncList <- list(coord1, coord3),[object Object],[object Object],[object Object],rl{ scheme schemeParam ======== ============= linear NA log NA geometric NA mult-power NA add-power $\ge$ 0 reciprocal NA exponential $\ge$ 0 tangent $\ge$ 0 }

We recommended using scheme = 'exponential' and schemeParam in [0.3, 0.5].,[object Object],[object Object],[object Object],[object Object],[object Object]

References

Gopi Goswami and Jun S. Liu (2007). On learning strategies for evolutionary Monte Carlo. Statistics and Computing 17:1:23-38.

See Also

placeTempers, parallelTempering, evolMonteCarlo

Examples

coord1        <- function (xx) { xx[1] }
ss            <- function (xx) { sum(xx) }
pp            <- function (xx) { prod(xx) }
statsFuncList <- list(coord1, ss, pp)
maxTemperObj  <-
    with(VShapedFuncGenerator(-13579),
         findMaxTemper(nIters            = 15000,
                       statsFuncList     = statsFuncList,
                       temperLadder      = c(20, 15, 10, 5, 1),
                       startingVals      = c(0, 0),
                       logTarDensFunc    = logTarDensFunc,
                       MHPropNewFunc     = MHPropNewFunc,
                       levelsSaveSampFor = seq_len(5),
                       doFullAnal        = TRUE,
                       verboseLevel      = 1))
print(maxTemperObj)
print(names(maxTemperObj))
with(maxTemperObj,
 {
     par(mfcol = c(3, 3))
     for (ii in seq_along(levelsSaveSampFor)) {
         main <- paste('temper:', round(temperLadder[levelsSaveSampFor[ii]], 3))
         plot(draws[ , , ii],
              xlim = c(-10, 25),
              ylim = c(-10, 10),
              pch  = '.',
              ask  = FALSE,
              main = as.expression(main),
              xlab = as.expression(substitute(x[xii], list(xii = 1))),
              ylab = as.expression(substitute(x[xii], list(xii = 2))))   
     }
 })