#' Conditional Particle filter via Sequential Importance Sampling with Resampling
#'
#' Runs a conditional particle filter on a given Non-Linear State Space models
#'
#' Warning: the resampling is Multinomial. Residual will bias the sampler, due to the
#' way we overried the Nth particle by the conditioned trajectory.
#'
#' @param x Trajectory on which to condition
#' @param ... same as classical sisr
#' @return A list with the same components as SISR, plus the components:
#' \item{x}{Array (T, D) of the new selected trajectory}
cpf.sisr <- function (x,nlss,y,N,
proposal.rnd=prior.rnd,
proposal.logpdf=prior.logpdf,
resampling=MultinomialR,
initial.proposal.rnd=initial.rnd,
initial.proposal.logpdf=initial.logpdf
) {
T <- length(y)
p <- array(dim=c(T,N,attr(nlss,"spaces")$dimx))
lw <- array(dim=c(T,N)); w <- array(dim=c(T,N))
a <- array(dim=c(T,N))
particles <- array(dim=c(N,attr(nlss,"spaces")$dimx))
ancestors <- 1:N
particles[,] <- initial.proposal.rnd(nlss, N=N, y[1,])
# Insert the conditioned particle at position N
particles[N,] <- x[1,]
if(!any(is.na(y[1,])))
logweights <- initial.logpdf(nlss, particles) - initial.proposal.logpdf(nlss, particles, y[1,], t=1) + loclike.logpdf(nlss, particles, y[1,])
else
logweights <- array(0,dim=c(1,N))
weights <- normalized.exponential(logweights)
p[1,,] <- particles; lw[1,] <- logweights; w[1,] <- weights; a[1,] <- ancestors
if (T > 1)
for (t in 2:T) {
# Resampling is optional and can be triggered by, e.g., a test for a low ESS
ancestors <- resampling(weights, N)
logweights <- array(0,dim=c(1,N))
xpast <- particles[ancestors,,drop=FALSE]
particles[,] <- proposal.rnd(nlss, xpast, y=y[t,], t=t)
# Insert the conditioned particle at position N
particles[N,] <- x[t,]
# Sample its ancestor
inserted.ancestors.logweights <- lw[t-1,] + prior.logpdf(nlss, p[t-1,,], x[t,], t=t)
inserted.ancestors.weights <- normalized.exponential(inserted.ancestors.logweights)
ancestors[N] <- resampling(inserted.ancestors.weights, 1)
xpast[N,] <- p[t-1,ancestors[N],]
if(!any(is.na(y[t])))
logweights <- loclike.logpdf(nlss, particles, y=y[t,], t=t)
logweights <- logweights +
prior.logpdf(nlss, xpast, particles, t=t) -
proposal.logpdf(nlss, xpast, particles, y=y[t,], t=t)
weights <- normalized.exponential(logweights)
p[t,,] <- particles; lw[t,] <- logweights; w[t,] <- weights; a[t,] <- ancestors
}
# Sample one of the trajectories according to the final weights
i <- resampling(weights, 1)
for(t in T:1) {
x[t,] <- p[t,i,]
i <- a[t,i]
}
# Return the weighted sample
list(particles=p, logweights=lw, weights=w, ancestors=a, t=1:T, x=x, success=TRUE)
}
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.