auxiliaryParticleFilter {SMC} | R Documentation |
Function for doing auxiliary particle filtering given the state
equation (via generateNextStreamsFunc
), the stream
representative generation rule (via generateStreamRepsFunc
),
and the observation equation density (via
logObsDensFunc
).
auxiliaryParticleFilter(nStreams, nPeriods, dimPerPeriod, generateStreamRepsFunc, generateNextStreamsFunc, logObsDensFunc, resampCriterionFunc = NULL, resampFunc = NULL, summaryFunc = NULL, nMHSteps = 0, MHUpdateFunc = NULL, nStreamsPreResamp = NULL, returnStreams = FALSE, returnLogWeights = FALSE, verboseLevel = 0, ...)
See the sections Details, Required Functions and Optional Functions for explanation on the arguments and the return values of the following arguments that are themselves functions.
nStreams |
integer > 0. |
nPeriods |
integer > 0. |
dimPerPeriod |
integer > 0. |
generateStreamRepsFunc |
function of five arguments
(currentPeriod, lag1Streams, lag1LogWeights, streamIndices,
...) . |
generateNextStreamsFunc |
function of seven arguments
(currentPeriod, lag1Streams, lag1LogWeights, streamIndices,
streamReps, startingStreams, ...) . |
logObsDensFunc |
function of three arguments
(currentPeriod, currentStreams, ... ). |
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 >= 0. |
MHUpdateFunc |
function of six arguments
(currentPeriod, nMHSteps, currentStreams, lag1Streams,
lag1LogWeights, ...) . |
nStreamsPreResamp |
integer > 0. |
returnStreams |
logical . |
returnLogWeights |
logical . |
verboseLevel |
integer , a value >= 2 produces a
lot of output. |
... |
optional arguments to be passed to
generateStreamRepsFunc , generateNextStreamsFunc ,
logObsDensFunc , resampCriterionFunc ,
resampFunc , summaryFunc and MHUpdateFunc .
|
We introduce the following terms, which will be used in the sections Required Function and Optional Function below:
stream
dimPerPeriod
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: “auxiliaryParticleFilter”. |
time |
the time taken by the run. |
lag1Streams
nStreams
x dimPerPeriod
of streams for
currentPeriod - 1
.lag1LogWeights
nStreams
of
log weights corresponding to the streams in the argument matrix
lag1Streams
.streamIndices
nStreams
for
which the stream representatives (μ_t^k of Pitt and
Shephard, 1999) for currentPeriod
are to be generated. See
the sub-section Note: below.
nStreamIndices
x dimPerPeriod
. The rows of this matrix
contain the stream representative for period currentPeriod
,
given the state vectors to be found in the streamIndices
rows of the argument lag1Streams
matrix. Here
nStreamIndices
is the length of the argument
streamIndices
.
currentPeriod == 1
and currentPeriod > 1
inside of
it.currentPeriod
(i.e., f(α_t mid α_{t -
1})).streamIndices
to
1:nStreams
, i.e., stream representatives for all the
streams in the argument lag1Streams
matrix is
generated.
lag1Streams
nStreams
x dimPerPeriod
of streams for
currentPeriod - 1
.lag1LogWeights
nStreams
of
log weights corresponding to the streams in the argument matrix
lag1Streams
.streamIndices
nStreams
which are to be updated from currentPeriod -
1
to currentPeriod
.streamReps
nStreams
x dimPerPeriod
of the stream representatives
for currentPeriod
.startingStreams
nStreams
x dimPerPeriod
to be used for
currentPeriod = 1
. If this is NULL
, then the
function should provide a way to generate streams for
currentPeriod = 1
.
nStreamIndices
x dimPerPeriod
. The rows of this matrix
contain the state vectors for period currentPeriod
, given
the state vectors to be found in the streamIndices
rows of
the argument lag1Streams
matrix. Here nStreamIndices
is the length of the argument streamIndices
.
currentPeriod == 1
and currentPeriod > 1
inside of
it.streamIndices
such that nStreamIndices
takes either of the two values
nStreams
or nStreamsPreResamp
in different
ocassions.
currentStreams
dimPerPeriod
columns, the rows containing the streams for
currentPeriod
.
nCurrentStreams
,
where nCurrentStreams
refers to the number of rows of the
currentStreams
matrix argument. This vector contains the
observation equation density values for currentPeriod
in
the log scale, evaluated at the rows of currentStreams
.
nCurrentStreams
might be >=
nStreams
.
currentStreams
dimPerPeriod
columns, the rows containing the updated streams for
currentPeriod
.currentLogWeights
currentStreams
.
TRUE
or FALSE
reflecting the
decision of the resampling scheme implemented by this function.
currentLogWeights
, the other two arguments might come in
handy for implementing period or stream specific resampling
schemes.nStreamsPreResamp
> nStreams
, then this
function should always return TRUE
.
currentStreams
nStreams
x dimPerPeriod
. The rows of this matrix
contain the streams for period currentPeriod + 1
that were
resampled from those of the argument currentStreams
matrix,
which may contain >= nStreams
rows.currentLogWeights
nStreams
, associated with the streams that were resampled
in the returned currentStreams
matrix. Note, after the
resampling step, usually all the log weights are set to 0.
currentStreams
and currentLogWeights
. These entities
have different meanings, as explained above. For example, the
argument matrix currentStreams
could possibly have
>= nStreams
rows, whereas the returned
currentStreams
has exactly nStreams
number of
(resampled) streams in its rows.
currentStreams
nStreams
x dimPerPeriod
of streams for
currentPeriod
.currentLogWeights
currentStreams
.
dimSummPerPeriod
of summaries for currentPeriod
given the
currentStreams
and the currentLogWeights
.
nMHSteps
currentStreams
nStreams
x dimPerPeriod
of streams for
currentPeriod
.lag1Streams
nStreams
x dimPerPeriod
of streams for
currentPeriod - 1
.lag1LogWeights
nStreams
of
log weights corresponding to the streams in the argument matrix
lag1Streams
.
currentStreams
nStreams
x dimPerPeriod
. The rows of this matrix
contain the streams for period currentPeriod
that are
(possibly) MH-updated versions of the rows of the argument
currentStreams
matrix.acceptanceRates
nStreams
,
representing the acceptance rates of the nMHSteps
MH steps
for each of the streams in the rows of the argument
currentStreams
matrix.
nMHSteps
performs as many MH
steps on the rows of the argument currentStreams
matrix. This is done to reduce the possible degeneracy after the
resampling.
Using very small values (<= 1e3
) for nStreams
might not give reliable results.
The effect of leaving the default value NULL
for some of the
arguments above are as follows:
resampCriterionFunc
resampFunc
summaryFunc
dimPerPeriod
dimensions, is used.MHUpdateFunc
particleFilter
, there is no builtin Metropolis
Hastings updating function, which generates proposals for
currentPeriod
streams using those of currentPeriod -
1
. The user needs to implement this function if
nMHSteps
> 0.nStreamsPreResamp
nStreams
.
Also, the following point is worth noting:
resampCriterionFunc
, resampFunc
,
summaryFunc
This function returns a list with component called draw
. The
detailed description of this component, as promised in section
Value, is as follows. It is a list itself with the following
components:
summary
nPeriods
x dimSummPerPeriod
.propUniqueStreamIds
nPeriods
. The values are either proportions of unique
streams accpeted (at each period) if resampling was done or
NA
.streams
nStreams
x dimPerPeriod
x
nPeriods
. This is returned if returnStreams = TRUE
.logWeights
nStreams
x nPeriods
. This is returned if
returnLogWeights = TRUE
.acceptanceRates
nStreams
x nPeriods
. This is returned if
nMHSteps > 0
.
Gopi Goswami goswami@stat.harvard.edu
Michael K. Pitt and Meil Shephard (1999). Filtering via Simulation: Auxiloary Particle Filters. Journal of the American Statistical Association 94(446): 590-599.
MSObj <- MarkovSwitchingFuncGenerator(-2468) smcObj <- with(MSObj, { auxiliaryParticleFilter(nStreams = 5000, nPeriods = nrow(yy), dimPerPeriod = ncol(yy), generateStreamRepsFunc = generateStreamRepsFunc, generateNextStreamsFunc = generateNextStreamsFunc, logObsDensFunc = logObsDensFunc, 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$summary[1, ]), main = expression('The underlying regimes and their estimates'), cex.main = 0.8, xlab = 'period', ylab = 'regime means', cex.lab = 0.8) lines(as.ts(mu), col = 2, lty = 2) }) MSObj <- MarkovSwitchingFuncGenerator(-8642) smcObj <- with(MSObj, { auxiliaryParticleFilter(nStreams = 5000, nPeriods = nrow(yy), dimPerPeriod = ncol(yy), generateStreamRepsFunc = generateStreamRepsFunc, generateNextStreamsFunc = generateNextStreamsFunc, logObsDensFunc = logObsDensFunc, returnStreams = TRUE, returnLogWeights = TRUE, verboseLevel = 1) }) print(smcObj) print(names(smcObj)) with(c(smcObj, MSObj), { par(mfcol = c(2, 1)) plot(as.ts(yy), main = expression('The data and the underlying regimes'), cex.main = 0.8, xlab = 'period', ylab = 'data and the regime means', cex.lab = 0.8) lines(as.ts(mu), col = 2, lty = 2) plot(as.ts(draws$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) })