w_mixEM {ashr}

Estimate mixture proportions of a mixture model by EM algorithm (weighted version)

Description

Given the individual component likelihoods for a mixture model, and a set of weights, estimates the mixture proportions by an EM algorithm.

Usage

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

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).

weights

an n vector of weights

control

A list of control parameters for the SQUAREM algorithm, default value is set to be control.default=list(K = 1, method=3, square=TRUE, step.min0=1, step.max0=1, mstep=4, kr=1, objfn.inc=1,tol=1.e-07, maxiter=5000, trace=FALSE).

Details

Fits a k component mixture model

f(x|\pi)= \sum_k \pi_k f_k(x)

to independent and identically distributed data x_1,\dots,x_n with weights w_1,\dots,w_n. Estimates mixture proportions \pi by maximum likelihood, or by maximum a posteriori (MAP) estimation for a Dirichlet prior on \pi (if a prior is specified). Here the log-likelihood for the weighted data is defined as l(\pi) = \sum_j w_j log f(x_j | \pi). Uses the SQUAREM package to accelerate convergence of EM. Used by the ash main function; there is no need for a user to call this function separately, but it is exported for convenience.

Value

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