#' State probabilities
#'
#' For a given model, computes the probability of the process being in the different states
#' at each time point.
#'
#' @param m A \code{moveHMM} object.
#'
#' @return The matrix of state probabilities, with element [i,j] the probability
#' of being in state j in observation i.
#'
#' @examples
#' # m is a moveHMM object (as returned by fitHMM), automatically loaded with the package
#' m <- example$m
#'
#' sp <- stateProbs(m)
#'
#' @references
#' Zucchini, W. and MacDonald, I.L. 2009.
#' Hidden Markov Models for Time Series: An Introduction Using R.
#' Chapman & Hall (London).
#'
#' @export
stateProbs <- function(m)
{
if(!is.moveHMM(m))
stop("'m' must be a moveHMM object (as output by fitHMM)")
data <- m$data
nbStates <- ncol(m$mle$stepPar)
nbAnimals <- length(unique(data$ID))
if(nbStates==1)
stop("No states to decode (nbStates=1)")
nbObs <- nrow(data)
la <- logAlpha(m) # forward log-probabilities
lb <- logBeta(m) # backward log-probabilities
stateProbs <- matrix(NA,nbObs,nbStates)
aInd <- NULL
for(i in 1:nbAnimals)
aInd <- c(aInd,max(which(data$ID==unique(data$ID)[i])))
for(i in nbObs:1){
if(any(i==aInd)){
c <- max(la[i,]) # cancels out below ; prevents numerical errors
llk <- c + log(sum(exp(la[i,]-c)))
}
stateProbs[i,] <- exp(la[i,]+lb[i,]-llk)
}
return(stateProbs)
}
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