#'Calculate posterior mixture proportions
#'@param llmat Log likelihood matrix
#'@param pihat Prior probabilities (possibly estimated)
#'@return A k by p matrix of probabilities. Columns sum to 1.
#'@export
mixture_posterior <- function(llmat, pihat){
llmat <- apply(llmat, 1, function(x){x-max(x)})
matrix_lik <- exp(llmat)
pi1 <- pihat*matrix_lik
pi1 = apply(pi1, 2, ashr:::normalize)
return(pi1)
}
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