Builds an MCEM algorithm from a given NIMBLE model
Takes a NIMBLE model and builds an MCEM algorithm for it. The user must specify which latent nodes are to be integrated out in the E-Step.
All other stochastic non-data nodes will be maximized over. If the nodes do not have positive density on the entire real line, then box constraints can be used
to enforce this.
The M-step is done by a nimble MCMC sampler. The E-step is done by a call to R's optim with method = 'L-BFGS-B' if the nodes are constrainted, or method = 'BFGS' if the nodes are unconstrained.
buildMCEM(model, latentNodes, burnIn = 500, mcmcControl = list(adaptInterval = 100), boxConstraints = list(), buffer = 10^-6, alpha = 0.25, beta = 0.25, gamma = 0.05, C = 0.001, numReps = 300, forceNoConstraints = FALSE, verbose = TRUE)
model |
a nimble model |
latentNodes |
character vector of the names of the stochastic nodes to integrated out. Names can be expanded, but don't need to be. For example, if the model contains
|
burnIn |
burn-in used for MCMC sampler in E step |
mcmcControl |
list passed to |
boxConstraints |
list of box constraints for the nodes that will be maximized over. Each constraint is a list in which the first element is a character vector of node names to which the constraint applies and the second element is a vector giving the lower and upper limits. Limits of |
buffer |
A buffer amount for extending the boxConstraints. Many functions with boundary constraints will produce |
alpha |
probability of a type one error - here, the probability of accepting a parameter estimate that does not increase the likelihood. Default is 0.25. |
beta |
probability of a type two error - here, the probability of rejecting a parameter estimate that does increase the likelihood. Default is 0.25. |
gamma |
probability of deciding that the algorithm has converged, that is, that the difference between two Q functions is less than C, when in fact it has not. Default is 0.05. |
C |
determines when the algorithm has converged - when C falls above a (1-gamma) confidence interval around the difference in Q functions from time point t-1 to time point t, we say the algorithm has converged. Default is 0.001. |
numReps |
number of bootstrap samples to use for asymptotic variance calculation. |
forceNoConstraints |
avoid any constraints even from parameter bounds implicit in the model structure (e.g., from dunif or dgamma distributions); setting this to TRUE might allow MCEM to run when the bounds of a parameter being maximized over depend on another parameter. |
verbose |
logical indicating whether to print additional logging information. |
buildMCEM calls the NIMBLE compiler to create the MCMC and objective function as nimbleFunctions. If the given model has already been used in compiling other nimbleFunctions, it is possible you will need to create a new copy of the model for buildMCEM to use.
Uses an ascent-based MCEM algorithm, which includes rules for automatically increasing the number of MC samples as iterations increase, and for determining when convergence has been reached. Constraints for parameter values can be provided. If constraints are not provided, they will be automatically determined by NIMBLE. Initial values for the parameters are taken to be the values in the model at the time buildMCEM is called, unless the values in the compiled model are changed before running the MCEM.
an R list with two elements:
run A function that when called runs the MCEM algorithm. This function takes the arguments listed in run Arguments below.
estimateCov An EXPERIMENTAL function that when called estimates the asymptotic covariance of the parameters. The covariance is estimated using the method of Louis (1982).
This function takes the arguments listed in estimateCov Arguments below.
run ArgumentsinitM
starting number of iterations for the algorithm.
estimateCov ArgumentsMLEs
named vector of MLE values. Must have a named MLE value for each stochastic, non-data, non-latent node. If the run() method has alread been called,
MLEs do not need to be provided.
useExistingSamples
logical argument. If TRUE and the run() method has previously been called, the covariance estimation will use MCMC samples from the last step of the MCEM algorithm.
Otherwise, an MCMC algorithm will be run for 10,000 iterations, and those samples will be used. Defaults to FALSE.
Clifford Anderson-Bergman and Nicholas Michaud
Caffo, Brian S., Wolfgang Jank, and Galin L. Jones (2005). Ascent-based Monte Carlo expectation-maximization. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(2), 235-251.
Louis, Thomas A (1982). Finding the Observed Information Matrix When Using the EM Algorithm. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 44(2), 226-233.
## Not run:
pumpCode <- nimbleCode({
for (i in 1:N){
theta[i] ~ dgamma(alpha,beta);
lambda[i] <- theta[i]*t[i];
x[i] ~ dpois(lambda[i])
}
alpha ~ dexp(1.0);
beta ~ dgamma(0.1,1.0);
})
pumpConsts <- list(N = 10,
t = c(94.3, 15.7, 62.9, 126, 5.24,
31.4, 1.05, 1.05, 2.1, 10.5))
pumpData <- list(x = c(5, 1, 5, 14, 3, 19, 1, 1, 4, 22))
pumpInits <- list(alpha = 1, beta = 1,
theta = rep(0.1, pumpConsts$N))
pumpModel <- nimbleModel(code = pumpCode, name = 'pump', constants = pumpConsts,
data = pumpData, inits = pumpInits)
# Want to maximize alpha and beta (both which must be positive) and integrate over theta
box = list( list(c('alpha','beta'), c(0, Inf)))
pumpMCEM <- buildMCEM(model = pumpModel, latentNodes = 'theta[1:10]',
boxConstraints = box)
MLEs <- pumpMCEM$run(initM = 1000)
cov <- pumpMCEM$estimateCov()
## End(Not run)
# Could also use latentNodes = 'theta' and buildMCEM() would figure out this means 'theta[1:10]'Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.