Expectation maximization - Beta and Uniform Distributions

This function calculates the log-likelihood using the expectation maximization algorithm with Nelder-Mead numerical optimization and beta distribution with one uniform mixture.

Usage

emstepBU(parmlist, xi, niter, epsilon, trunc, type = "free", glreturn = FALSE)

Arguments

parmlist

A list containing initial alpha, mean, and variance values.

xi

List of observations, in this case allele frequencies.

niter

Max number of iterates.

epsilon

Epsilon value for convergence tolerance. When the absolute delta log-likelihood is below this value, convergence is reached.

trunc

List of two values representing the lower and upper bounds, \(c_{L}\) and \(c_{U}\).

type

String indicating model type. Options: "free" (estimated parameter(s): alpha, mean, and variance), "fixed" (estimated parameter(s): alpha), "fixed_2" (estimated parameter(s): alpha and variance), or "fixed_3" (estimated parameter(s): variance). If avec is length of 1, fixed and fixed_3 will not be able to return a log-likelihood.

glreturn

Logical statement, if true, the function will return the log-likelihood, negative log-likelihood, optimized parameter values, number of iterates, and the probability of each observation belonging to each mixture model. If false, the function will return the log-likelihood, negative log-likelihood, optimized parameter values, and number of iterates.

Value

List of elements including the log likelihood, the negative log likelihood, the number of iterates, and the optimized parameter values.

Examples

if(exists("crazy")){
  xi <- (xm[,2]/xm[,1])
  p = list(avec = c(0.18, 0.18, 0.18, 0.18, 0.18, 0.1),
           mvec = c(0.20, 0.33, 0.50, 0.67, 0.80),
           svec = c(0.01, 0.01, 0.01, 0.01, 0.01));
  mout <- emstepBU(p,
                   xi,
                   niter = 100,
                   epsilon = 0.1,
                   trunc = c(0.0,0.0))
}