Tid: 9 februari 1998 kl 1515-1700

Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!

Föredragshållare: Tobias Rydén, Matematisk statistik, Lunds Tekniska Högskola. (Publikationslista)

Titel: Bayesian inference in hidden Markov models through jump Markov Chain Monte Carlo

Sammanfattning: A hidden Markov model (HMM) is a bivariate stochastic process tex2html_wrap_inline6 such that

(i) tex2html_wrap_inline8 is a finite state Markov chain

(ii) given tex2html_wrap_inline8 , the process tex2html_wrap_inline12 is a sequence of conditionally independent random variables with the conditional distribution of tex2html_wrap_inline14 depending on tex2html_wrap_inline16 only.

The chain tex2html_wrap_inline8 is generally not observable, hence the word `hidden', so that inference has to be based on tex2html_wrap_inline12 alone.

HMMs have during the last decade become widely spread for modelling sequences of weakly dependent random variables with applications in areas like speech processing, communication networks, biochemistry, biology, medicine, econometrics, environmetrics, etc. Sometimes the hidden Markov chain tex2html_wrap_inline8 does indeed exist, so that the physical nature of the problem suggests the use of an HMM, in other cases HMMs just provide a good fit to data.

One of the most difficult problems in inference for HMM is to estimate the number of states, d say, of tex2html_wrap_inline8. Classical approaches to this problem include likelihood ratio tests and penalized likelihoods (AIC/BIC). In this talk we present a Bayesian approach: by placing a prior on the unknown d we obtain a posterior distribution for d and the other parameters of the model. This distribution is analytically untractable but can be explored using jump Markov chain Monte Carlo algorithms. Finally an application to stock market data is presented.

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