Organizer:

Denkmar Böhning, boehning@zedat.fu-berlin.de

Speakers

8:15 a.m.
Computing Issues for the EM Algorithm in Mixture Models
Geoffrey McLachlan, The University of Queensland

8:45 a.m.
Inferential Problems in Mixture Models: the EM Algorithm and the Likelihood Ratio Test
Wilfried Seidel, Universität der Bundeswehr Hamburg
Keywords: Mixture Models, Likelihood Ratio Test, EM Algorithm, Global Maximization, Bootstrap Test, Critical Values

Iterative methods for maximizing the likelihood in mixture models may depend strongly on the details of their implementation. As these effects are particularly severe if the data come from the "wrong" model, likelihood ratio tests for the number of components are heavily affected by them: In a mixture of exponentials model we demonstrate that different starting strategies and even stopping rules for the EM algorithm result in completely different tests.

These observations have strong practical implications. Ignoring them can result in wrong critical values and therefore in tests with completely wrong levels. On the other hand, they can be used to construct computationally simple and powerful tests: A subglobal version of the EM that is started from only one suitably chosen initial value and that often fails to find the global maximum under the null hypothesis results in a considerably better power than a test based on global maximization. This is of advantage especially in situations, where under the null hypothesis the quantiles of the test statistic depend on the unknown population parameters and therefore have to be simulated under the estimated parameters each time the test is performed.

9:15 a.m.
Computational Methods for Non-parametric Maximum Likelihood Estimation of Mixtures
Edward Susko, Dalhousie University
(with John D. Kalbfleisch and Jiahua Chen, University of Waterloo) Keywords: Mixture model, Nonparametric, Statistical Computing, Semi-infinite programming

Calculating the nonparametric maximum likelihood estimate of a mixing distribution is computationally intensive. There are a number of existing algorithms available to obtain the maximum likelihood estimator but one class of methods that has not receieved a great deal of attention is the use of semi-infinite programming algorithms. We will indicate how semi-infinite programming arises for the mixture problem. An algorithm will be presented for the mixture problem and the results of some numerical experiments will be reported.

9:45 a.m.
Floor contributions: Denkmar Böhning