mixIP function

Estimate mixture proportions of a mixture model by Interior Point method

Given the individual component likelihoods for a mixture model, estimates the mixture proportions.

mixIP(matrix_lik, prior, pi_init = NULL, control = list(), weights = NULL)

Arguments

• matrix_lik,: a n by k matrix with (j,k)th element equal to $f_k(x_j)$.
• prior,: a k vector of the parameters of the Dirichlet prior on $\pi$. Recommended to be rep(1,k)
• pi_init,: the initial value of $\pi$ to use. If not specified defaults to (1/k,...,1/k).
• control: A list of control parameters to be passed to REBayes::KWDual
• weights: weights to be assigned to the observations (an n vector)

Returns

A list, including the estimates (pihat), the log likelihood for each interation (B) and a flag to indicate convergence

Details

Optimizes

subject to pi_k non-negative and sum_k pi_k = 1. Here

is a penalty function h(pi) = sum_k (prior_k-1) log pi_k. Calls REBayes::KWDual in the REBayes package, which is in turn a wrapper to the mosek convex optimization software. So REBayes must be installed to use this. Used by the ash main function; there is no need for a user to call this function separately, but it is exported for convenience.