mixVBEM function

Estimate posterior distribution on mixture proportions of a mixture model by a Variational Bayes EM algorithm

Given the individual component likelihoods for a mixture model, estimates the posterior on the mixture proportions by an VBEM algorithm. Used by the ash main function; there is no need for a user to call this function separately, but it is exported for convenience.

mixVBEM(matrix_lik, prior, pi_init = 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 the posterior parameters. If not specified defaults to the prior parameters.
• 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).

Returns

A list, whose components include point estimates (pihat), the parameters of the fitted posterior on $\pi$ (pipost), the bound on the log likelihood for each iteration (B) and a flag to indicate convergence (converged).

Details

Fits a k component mixture model

to independent and identically distributed data $x_1,\dots,x_n$. Estimates posterior on mixture proportions $\pi$ by Variational Bayes, with a Dirichlet prior on $\pi$. Algorithm adapted from Bishop (2009), Pattern Recognition and Machine Learning, Chapter 10.