Given the individual component likelihoods for a mixture model, and a set of weights, estimates the mixture proportions by an EM algorithm.
w_mixEM(matrix_lik, prior, pi_init = NULL, weights = NULL, control = list())A list, including the estimates (pihat), the log likelihood for each interation (B) and a flag to indicate convergence
a n by k matrix with (j,k)th element equal to \(f_k(x_j)\).
a k vector of the parameters of the Dirichlet prior on \(\pi\). Recommended to be rep(1,k)
the initial value of \(\pi\) to use. If not specified defaults to (1/k,...,1/k).
an n vector of weights
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).
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.