# computes posterior probabilities and incomplete-data
# log-likelihood for mixture models
# logdensity : K*P matrix containing the conditinal log-densities for each segment
# phi : parameters of the mixture
# tau : K*P matrix containing posterior probabilities of membership to clusters
Estep <- function (logdensity,phi){
K = nrow(logdensity)
P = ncol(logdensity)
tau = repmat( t (log( phi[(2*P+1):(3*P)] )),K,1)+logdensity
tau_max = apply(tau,1,max)
tau = exp(tau-repmat(tau_max,1,P))
lvinc = sum(log( apply(tau,1,sum)) + tau_max)
tau = tau / repmat( apply(tau,1,sum) ,1,P)
invisible(list(tau,lvinc))
}
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