- 547863post.pdf (2M)

## Forfatter(e)

## Utgivelsesdato

2010-06-17

## Serie/Rapportnr.

Computational Statistics & Data Analysis;55 (1)

## Utgiver

Elsevier

## Dokumenttype

## Sammendrag

A hidden Markov model with two hidden layers is considered. The bottom layer is a Markov
chain and given this the variables in the second hidden layer are assumed conditionally
independent and Gaussian distributed. The observation process is Gaussian with mean
values that are linear functions of the second hidden layer. The forward backward
algorithm is not directly feasible for this model as the recursions result in a mixture
of Gaussian densities where the number of terms grows exponentially with the length
of the Markov chain. By dropping the less important Gaussian terms an approximate
forward backward algorithm is defined. Thereby one gets a computationally feasible
algorithm that generates samples from an approximation to the conditional distribution of
the unobserved layers given the data. The approximate algorithm is also used as a proposal
distribution in a Metropolis Hastings setting, and this gives high acceptance rates and good
convergence and mixing properties. The model considered is related to what is known as
switching linear dynamical systems. The proposed algorithm can in principle also be used
for these models and the potential use of the algorithm is therefore large. In simulation
examples the algorithm is used for the problem of seismic inversion. The simulations
demonstrate the effectiveness and quality of the proposed approximate algorithm.

## Emneord

## Versjon

Postprint version of article published by Elsevier. Original article can be found at URL: http://dx.doi.org/10.1016/j.csda.2010.06.008

## Permanent URL

- http://hdl.handle.net/10642/564