Galin Jones
School of Statistics
University of Minnesota
Wednesday, November 20, 2002
3:30 PM
Moos Tower 2-650
Minneapolis Campus
Abstract:
The EM algorithm is a popular tool for maximizing likelihood functions in
the presence of missing data. Unfortunately, in many practical problems EM requires
the evaluation of analytically intractable and high-dimensional integrals. The
Monte Carlo EM (MCEM) algorithm is the natural extension of EM that employs
Monte Carlo methods to estimate the relevant integrals. Unfortunately, naive
application of MCEM does not typically result in an algorithm that inherits
the desirable properties enjoyed by EM.
In this talk, I will propose a data-driven automated MCEM algorithm that attempts to mimic the underlying deterministic version. An important feature of the algorithm is that, regardless of the dimension of the parameter space, all algorithmic decisions based on the Monte Carlo sample rely on a univariate function. This simplifies the algorithm and allows use of either classical Monte Carlo or Markov chain Monte Carlo approximations to the E-step within a unified framework. These techniques will be illustrated with several examples, including one that shows how to use MCEM in conjunction with deterministic EM to obtain a hybrid algorithm that converges more quickly than deterministic EM alone. This is joint work with Brian Caffo (Johns Hopkins) and Wolfgang Jank (University of Maryland).