#PostProbT <- function(x,std_err,df,support,mix.prop) {
# n <- length(x)
# T <- length(support)
# z <- .C("postprobT", as.double(x), as.double(std_err),
# as.double(df),as.double(support), as.double(mix.prop),
# as.integer(n), as.integer(T), double(T),
# post = double(n*T), loglik = double(1), PACKAGE = "rvalues")
# ans <- list()
# ans$postprobs <- matrix(z$post, nrow=n)
# ans$loglik <- z$loglik
# return(ans)
#}
PostProbT <- function(x, std_err, df, support, mix.prop) {
### Amat is nsupport x n matrix
dff <- (df + 1)/2
ResidMat <- (outer(x, support, FUN="-")^2)/(std_err^2)
Amat <- t(exp(-dff*log(1 + ResidMat/df)))
B <- mix.prop*Amat
lik <- colSums(B)
PP <- t(B)/lik
ans <- list()
ans$loglik <- sum(log(lik))
ans$postprobs <- PP
return(ans)
}
NPestT = function(x,std_err,df,maxiter,tol,nmix) {
### This function takes an initial estimate of the mixing distribution
### and the loc.scale matrix and returns a final estimate of the
### mixing distribution using the EM algorithm.
### Also, it returns an indicator of convergence.
### 0 - did converge. 1 - did not converge.
### densmat should have dimensions [n,T]
### densmat[i,j] - p(X_{j}|\theta_{i})
n <- length(x)
grid.to <- max(x)
grid.from <- min(x)
if(is.null(nmix)) {
if(n <= 200) {
nmix <- n
}
else{
## Number of mixture components grows according to
## f(x) = 200 + 5*log(x)*[(x - 200)^(.3)]
nn <- n - 200
nmix <- 200 + ceiling(5*exp(.3*log(nn))*log(nn))
}
}
log.lik <- rep(0,maxiter + 1)
counter <- 0
support <- c(1:nmix)*(grid.to/nmix)
mix.prop <- rep(1/nmix,nmix)
ss <- 1/(std_err^2)
tmp <- PostProbT(x,std_err,df,support,mix.prop)
PP <- tmp$postprobs
log.lik[1] <- tmp$loglik
done <- FALSE
aa <- rep(1/2, n)
for(k in 1:maxiter) {
mix.prop <- colMeans(PP)
### EM update for the support is based on assuming that (conditional on cluster assignment)
### xi ~ N(mu_k, (std_erri^2)/ai), where the latent variables ai ~ Gamma(df/2, df/2) (rate form of gamma)
bb <- ss*aa
support <- as.vector(crossprod(PP,x*bb)/crossprod(PP, bb))
tmp <- PostProbT(x,std_err,df,support,mix.prop)
PP <- tmp$postprobs
log.lik[k+1] <- tmp$loglik
done <- (abs((log.lik[k+1] - log.lik[k])/log.lik[k]) < tol)
counter <- counter + 1
if(done) {
break
}
residMat <- (outer(x, support, FUN="-")^2)*ss
rsumsPP <- rowSums(PP)
aa <- ((df-1)*rsumsPP)/(rowSums(PP*residMat) + df*rsumsPP)
}
print(summary(support))
post.mean <- PP%*%support
log.lik <- log.lik[1:(counter+1)]
conv = ifelse(maxiter == counter,1,0)
return(list(mix.prop=mix.prop,support=support,convergence = conv,log.lik=log.lik,numiter=counter, post.mean=post.mean))
}
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