evolMonteCarlo {EMC} | R Documentation |
Given a multi-modal and multi-dimensional target density function, a (possibly asymmetric) proposal distribution and a temperature ladder, this function produces samples from the target using the evolutionary Monte Carlo algorithm.
Below sampDim
refers to the dimension of the sample space,
temperLadderLen
refers to the length of the temperature ladder,
and levelsSaveSampForLen
refers to the length of the
levelsSaveSampFor
.
evolMonteCarlo(nIters, temperLadder, startingVals, logTarDensFunc, MHPropNewFunc, logMHPropDensFunc = NULL, MHBlocks = NULL, MHBlockNTimes = NULL, moveProbsList = NULL, moveNTimesList = NULL, SCRWMNTimes = NULL, SCRWMPropSD = NULL, levelsSaveSampFor = NULL, nThin = 1, saveFitness = FALSE, verboseLevel = 0, ...)
nIters |
|
temperLadder |
|
startingVals |
|
logTarDensFunc |
|
MHPropNewFunc |
|
logMHPropDensFunc |
|
MHBlocks |
|
MHBlockNTimes |
|
moveProbsList |
named |
moveNTimesList |
named |
SCRWMNTimes |
|
SCRWMPropSD |
|
levelsSaveSampFor |
|
nThin |
|
saveFitness |
|
verboseLevel |
|
... |
optional arguments to be passed to |
MHPropNewFunc
and logMHPropDensFunc
The
MHPropNewFunc
and the logMHPropDensFunc
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)
.
The evolutionary Monte Carlo (EMC; Liang and Wong, 2001) algorithm is composed of the following moves:
MH | Metropolis-Hastings or mutation |
RC | real crossover |
SC | snooker crossover |
RE | (random) exchange |
The target oriented EMC (TOEMC; Goswami and Liu, 2007) algorithm has the following additional moves on top of EMC:
BCE | best chromosome exchange |
BIRE | best importance ratio exchange |
BSE | best swap exchange |
CE | cyclic exchange |
The current function could be used to run both EMC and TOEMC algorithms by specifying what moves to employ using the following variables.
moveProbsList
and moveNTimesList
The allowed
names for components of moveProbsList
and
moveNTimesList
come from the abbreviated names of the
moves above. For example, the following specifications are
valid:
moveProbsList = list(MH = 0.4, RC = 0.3, SC = 0.3)
moveNTimesList = list(MH = 1, RC = floor(temperLadderLen / 2), SC = floor(temperLadderLen / 2), RE = temperLadderLen)
SCRWMNTimes
and SCRWMPropSD
The conditional
sampling step of the snooker crossover (SC) move is done using
random walk Metropolis (RWM) with normal proposals;
SCRWMNTimes
and SCRWMPropSD
are the number of RWM
draws and the proposal standard deviation for the RWM step,
respectively. Note these variables are only required if the SC
move has positive probability in moveProbsList
or a
positive number of times in moveNTimesList
.
levelsSaveSampFor
By default, samples are saved and
returned for temperature level temperLadderLen
. The
levelsSaveSampFor
could be used to save samples from other
temperature levels as well (e.g., levelsSaveSampFor =
1:temperLadderLen
saves samples from all levels).
saveFitness
The term fitness refers to the function H(x), where the target density of interest is given by:
g(x) \propto \exp[ -H(x) / τ_{min} ]
H(x) is also known as the energy function. By default,
the fitness values are not saved, but one can do so by setting
saveFitness = TRUE
.
Below nSave
refers to ceil(nIters / nThin)
. This
function returns a list with the following components:
draws |
|
acceptRatios |
|
detailedAcceptRatios |
|
nIters |
the |
nThin |
the |
nSave |
as defined above. |
temperLadder |
the |
startingVals |
the |
moveProbsList |
the |
moveNTimesList |
the |
levelsSaveSampFor |
the |
time |
the time taken by the run. |
The effect of leaving the default value NULL
for some of the
arguments above are as follows:
logMHPropDensFunc
| the proposal density MHPropNewFunc is deemed symmetric.
|
MHBlocks
| as.list(1:sampDim) .
|
MHBlockNTimes
| rep(1, length(MHBlocks)) .
|
moveProbsList
| list(MH = 0.4, RC = 0.3, SC = 0.3) .
|
moveNTimesList
| list(MH = 1, RC = mm, SC = mm, RE = nn) , where
|
mm <- floor(nn / 2) and nn <- temperLadderLen .
|
|
SCRWMNTimes
| 1, if SC is used. |
SCRWMPropSD
| needs to be provided by the user, if SC is used. |
levelsSaveSampFor
| temperLadderLen .
|
Gopi Goswami goswami@stat.harvard.edu
Gopi Goswami and Jun S. Liu (2007). On learning strategies for evolutionary Monte Carlo. Statistics and Computing 17:1:23-38.
Faming Liang and Wing H.Wong (2001). Real-Parameter Evolutionary Monte Carlo with Applications to Bayesian Mixture Models. Journal of the American Statistical Association 96:653-666.
## Not run: samplerObj <- with(VShapedFuncGenerator(-13579), { allMovesNTimesList <- list(MH = 1, RC = 2, SC = 2, RE = 4, BIRE = 2, BCE = 2, BSE = 2, CE = 2) evolMonteCarlo(nIters = 2000, temperLadder = c(15, 6, 2, 1), startingVals = c(0, 0), logTarDensFunc = logTarDensFunc, MHPropNewFunc = MHPropNewFunc, moveNTimesList = allMovesNTimesList, SCRWMNTimes = 1, SCRWMPropSD = 3.0, levelsSaveSampFor = seq_len(4), verboseLevel = 1) }) print(samplerObj) print(names(samplerObj)) with(samplerObj, { print(detailedAcceptRatios) print(dim(draws)) par(mfcol = c(2, 2)) for (ii in seq_along(levelsSaveSampFor)) { main <- paste('temper:', round(temperLadder[levelsSaveSampFor[ii]], 3)) plot(draws[ , , ii], xlim = c(-5, 20), ylim = c(-8, 8), 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)))) } }) ## End(Not run)