Turner, Rolf

Hidden Markov models, probability tables and the Levenberg-Marquardt algorithm.

Department of Statistics, University of Auckland

The underlying problem is one of fitting hidden Markov models to sequences of discrete valued observations for which there is no appropriate parametric distribution. The distributions have to be specified non-parametrically via tables (one table for each state of the underlying Markov chain). I have tried fitting the models in the “usual” way via the EM algorithm, and also tried a “brute force” method whereby the likelihood is maximised using the nlm() function. Both approaches proved unsatisfactory, so I implemented a Levenberg-Marquardt algorithm in this context. I had previously used the Levenberg-Marquardt algorithm to fit hidden Markov models in settings in which the observations are Poisson distributed. Conceptually it is straightforward to adapt the procedure to the non-parametric context. In this talk I will describe some of the challenges involved in working out the details. Once these details were dealt with, the LM algorithm turned out to be fast, effective and reliable. I will briefly present some of the results of a data analysis that makes use of this algorithm.