SMC (version 1.0)

sequentialMonteCarlo: The sequential Monte Carlo (SMC) algorithm

Description

Function for the doing sequential Monte Carlo algorithm given the propagation rule over time (via propagateFunc). This is the most general interface for implementing a new SMC strategy, by providing a new propagation rule.

Usage

sequentialMonteCarlo(nStreams,                     
                     nPeriods,                     
                     dimPerPeriod,                 
                     propagateFunc,             
                     resampCriterionFunc = NULL,   
                     resampFunc          = NULL,   
                     summaryFunc         = NULL,   
                     nMHSteps            = 0,      
                     MHUpdateFunc        = NULL,   
                     nStreamsPreResamp   = NULL,   
                     returnStreams       = FALSE,  
                     returnLogWeights    = FALSE,  
                     verboseLevel        = 0,      
                     ...)

Arguments

nStreams

integer $>$ 0.

nPeriods

integer $>$ 0.

dimPerPeriod

integer $>$ 0.

propagateFunc

function of six arguments (currentPeriod, nStreamsToGenerate, lag1Streams, lag1LogWeights, startingStreams, ...).

resampCriterionFunc

function of four arguments (currentPeriod, currentStreams, currentLogWeights, ...).

resampFunc

function of four arguments (currentPeriod, currentStreams, currentLogWeights, ...).

summaryFunc

function of four arguments (currentPeriod, currentStreams, currentLogWeights, ...).

nMHSteps

integer $\ge$ 0.

MHUpdateFunc

function of six arguments (currentPeriod, nMHSteps, currentStreams, lag1Streams, lag1LogWeights, ...).

nStreamsPreResamp

integer $>$ 0.

returnStreams

logical.

returnLogWeights

logical.

verboseLevel

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

...

optional arguments to be passed to propagateFunc, resampCriterionFunc, resampFunc, summaryFunc and MHUpdateFunc.

Value

• This function returns a list with the following components:
• draws
  a list with the following components: summary, propUniqueStreamIds, streams, logWeights, acceptanceRates. See the section Note for more details.
• nStreams
  the nStreams argument.
• nPeriods
  the nPeriods argument.
• dimPerPeriod
  the dimPerPeriod argument.
• nStreamsPreResamp
  the nStreamsPreResamp argument.
• nMHSteps
  the nMHSteps argument.
• filterType
  type of the filter: sequentialMonteCarlo.
• time
  the time taken by the run.

Warning

Using very small values ($\le$ 1e3) for nStreams might not give reliable results.

Details

We introduce the following terms, which will be used in the sections Required Function and Optional Function below:

[object Object],[object Object]

References

Jun S. Liu (2001). Monte Carlo strategies for scientific computing. Springer. Chapter 3.

Jun S. Liu and Rong Chen (1998). Sequential Monte Carlo methods for dynamical systems. Journal of the American Statistical Association 98(443): 1032-1044.

See Also

particleFilter, auxiliaryParticleFilter

Examples

MSObj  <- MarkovSwitchingFuncGenerator(-12345)
smcObj <-
    with(MSObj,
     {
         sequentialMonteCarlo(nStreams         = 5000,
                              nPeriods         = nrow(yy),
                              dimPerPeriod     = ncol(yy),
                              propagateFunc    = propagateFunc,
                              returnStreams    = TRUE,
                              returnLogWeights = TRUE,
                              verboseLevel     = 1)
     })
print(smcObj)
print(names(smcObj))
with(c(smcObj, MSObj),
 {
     par(mfcol = c(2, 1))
     plot(as.ts(yy),
          main     = expression('The data and the underlying regimes'),
          cex.main = 0.8,
          xlab     = 'period',
          ylab     = 'data and the regime means',
          cex.lab  = 0.8)
     lines(as.ts(mu), col = 2, lty = 2)
     plot(as.ts(draws$summary[1, ]),
          main     = expression('The underlying regimes and their estimates'),
          cex.main = 0.8,
          xlab     = 'period',
          ylab     = 'regime means',
          cex.lab  = 0.8)
     lines(as.ts(mu), col = 2, lty = 2)        
 })

MSObj  <- MarkovSwitchingFuncGenerator(-54321)
smcObj <-
    with(MSObj,
     {
         sequentialMonteCarlo(nStreams         = 5000,
                              nPeriods         = nrow(yy),
                              dimPerPeriod     = ncol(yy),
                              propagateFunc    = propagateFunc,
                              returnStreams    = TRUE,
                              returnLogWeights = TRUE,
                              verboseLevel     = 1)
     })
print(smcObj)
print(names(smcObj))
with(c(smcObj, MSObj),
 {
     par(mfcol = c(2, 1))
     plot(as.ts(yy),
          main     = expression('The data and the underlying regimes'),
          cex.main = 0.8,
          xlab     = 'period',
          ylab     = 'data and the regime means',
          cex.lab  = 0.8)
     lines(as.ts(mu), col = 2, lty = 2)
     plot(as.ts(draws$summary[1, ]),
          main     = expression('The underlying regimes and their estimates'),
          cex.main = 0.8,
          xlab     = 'period',
          ylab     = 'regime means',
          cex.lab  = 0.8)
     lines(as.ts(mu), col = 2, lty = 2)        
 })