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samplenuST = function(y, X, N, particles, priorList){
# Given the arguments, this function returns a population of MC draws for the values of the latent variable Nu, in the p-variate skew-t model.
n = nrow(y)
#
v = particles$v
rm(particles)
#
gdls = priorList$gdls
nulogpriors = priorList$nulogpriors
sumlogv = apply(log(v), 1, sum)
sumv = apply(v, 1, sum)
logProbs = matrix(0, N, length(gdls))
for(igdl in 1:length(gdls)){
gdl = gdls[igdl]
logProbs[,igdl] = nulogpriors[igdl] + n * gdl * log(gdl/2) / 2 - n * lgamma(gdl/2) +
(gdl/2-1) * sumlogv - gdl * sumv / 2
}
values = propdens = nuIndices = numeric(N)
for(inu in 1:N){
logprobs = logProbs[inu,]
nuprobs = exp(logprobs) / sum(exp(logprobs))
nuIndices[inu] = sample(1:length(gdls), size=1, prob=nuprobs)
values[inu] = gdls[nuIndices[inu]]
propdens[inu] = log(nuprobs[nuIndices[inu]])
}
return(list(values=values, log.dq=propdens))
}
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