Article de revue avec comité de lecture (2)
BARDEL Noémie, DESBOUVRIES François
Exact bayesian prediction in a class of Markov-switching models. Methodology and computing in applied probability, march 2012, vol. 14, n° 1, pp. 125-134
abstract
Jump-Markov state-space systems (JMSS) are widely used in statistical signal processing. However as is well known Bayesian restoration in JMSS is an NP-hard problem, so in practice all inference algorithms need to resort to some approximations. In this paper we focus on the computation of the conditional expectation of the hidden variable of interest given the available observations, which is optimal from the Bayesian quadratic risk viewpoint. We show that in some stochastic systems, namely the Partially Pairwise Markov-switching Chains (PPMSC) and Trees (PPMST), no approximation scheme is actually needed since the conditional expectation of interest (be it either in a filtering or prediction problem) can be computed exactly and in a number of operations linear in the number of observations.
LAPUYADE-LAHORGUE Jérôme, PIECZYNSKI Wojciech
Unsupervised segmentation of hidden semi-Markov non-stationary chains. Signal processing, january 2012, vol. 92, n° 1, pp. 29-42
abstract
The Bayesian segmentation using Hidden Markov Chains (HMC) is widely used in various domains such as speech recognition, acoustics, biosciences, climatology, text recognition, automatic translation and image processing. On the one hand, hidden semi-Markov chains (HSMC), which extend HMC, have turned out to be of interest in many situations and have improved HMC-based results. On the other hand, the case of non-stationary data can pose an important problem in real-life situations, especially when the model parameters have to be estimated. The aim of this paper is to consider these two extensions simultaneously: we propose using a particular triplet Markov chain (TMC) to deal with non-stationary hidden semi-Markov chains. In addition, we consider a recent particular HSMC having the same computation complexity as the classical HMC. We propose a related parameter estimation method and the resulting unsupervised Bayesian segmentation is validated through experiments; in particular, a real radar image segmentations are provided.
