PLACE:

SPEAKER:
Richard Levine & Juanjuan Fan
University of California at Davis

PART 1

SPEAKER:
Richard Levine
University of California at Davis

TITLE:
Implementations of the Monte Carlo EM alggorithm

ABSTRACT:
The EM algorithm has become a popular tool for obtaining maximum likelihood estimates under models that yield analytically formidable likelihood equations. The Monte Carlo EM (MCEM) is a modification of the EM algorithm where the expectation in the E-step is computed numerically through Monte Carlo simulations. While the Monte Carlo estimate presents a tractable solution to problems where the E-step is not available in closed form, the additional computational cost in obtaining the Monte Carlo sample must be considered. In this talk we will present implementations of the MCEM algorithm with random variates taken from Markov chain Monte Carlo (MCMC) schemes such as the Gibbs and Metropolis-Hastings samplers. In particular, we will discuss how to save simulation time through importance sampling whereby samples drawn during previous EM iterations are recycled. We will also consider how to gauge the Monte Carlo sample size through a study o the convergence properties and dependence structure of the Markov chain induce by these sampling plans. We will motivate our problem, introduce the MCEM algorithm, and apply our results through the analysis of a data set studying mating success between two species of salamanders.

PART 2

SPEAKER:
Juanjuan Fan
University of California at Davis

TITLE:
A Class of Weighted Dependence Measures for Bivariate Failure Time Data

ABSTRACT:
We consider a class of summary measures of the dependence between a pair of failure time variables over a finite follow-up region. The class consists of measures that are weighted averages of local dependency measures, and includes the cross ration measure and finite region version of Kendall's tau. Special cases are also identified that can avoid the need to estimate the bivariate survivor function and that admit explicit variance estimators. Nonparametric estimators of such dependency measures are proposed and are shown to be consistent and asymptotically normal with variances that can be consistently estimated. Properties of selected estimators are evaluated in a simulation study, and the method is illustrated through an analyses of Australian Twin Study data.

COFFEE:  3:45p.m.