Student Seminar Series - March 8, 2005
University of Minnesota
School of Statistics
College of Liberal Arts
Monte
Carlo Methods for Maximum Likelihood Estimation in Hierarchical Models
Ronald Neath
Tuesday, March 8, 2005
1:30 PM, 47
Rapson Hall
Minneapolis, East Bank Campus
Refreshments at 1:00 PM
300 Ford Hall
Abstract
Statistical models with a hierarchical structure, such as
generalized linear mixed models (GLMMs), often yield likelihood
functions that depend on high-dimensional, analytically intractable
integrals. Likelihood-based inference, including maximum likelihood
estimation, will thus require specialized computational methods.
Deterministic optimization algorithms like Newton-Raphson or the EM
algorithm are typically impracticable in these problems.
In this talk we will introduce the Monte Carlo EM algorithm, in which
an intractable E-step is replaced by a Monte Carlo approximation. The
application of this method to hierarchical models requires simulation
from a distribution whose density is known only up to a normalizing
constant; the Metropolis-Hastings algorithm is a natural choice. We
illustrate the method on a logit-normal toy example, comparing the
performance of three different Metropolis-Hastings samplers.