*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
such that

**(i)** is a finite state Markov chain

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

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