Seminarium i matematisk statistik
fredagen den 24 mars 15.00 i MH:227

Søren Feodor Nielsen
Statistics Division
University of Copenhagen 

Titel:
Simulated EM algorithms: A comparison

Abstract:
The EM algorithm is a popular and useful algorithm for
finding the maximum likelihood estimator in incomplete
data problems. Each iteration of the algorithm consists
of two simple steps: An E-step, in which a conditional
expectation is calculated, and an M-step, where the
expectation is maximized. In some problems, however, the
EM algorithm cannot be applied since the conditional
expectation required in the E-step cannot be calculated.
Instead the expectation may be estimated by simulation. We
call this a simulated EM algorithm.
 
The simulations can be carried out in two different ways:
We can either draw new (independent) random variables in each
iteration, or we can "re-use the uniforms". Both versions of
the simulated EM algorithm lead to consistent, asymptotically
normal estimators of the unknown parameters. But there is a
number of theoretical and practical differences between the
two algorithms. 

The purpose of this talk is to give an introduction to simulated
EM algorithms and discuss the relative merits of the two versions.