Exact Bayesian Prediction in a Class of Markov-switching Models

Bardel, Noémie; Desbouvries, François

doi:10.1007/s11009-010-9189-4

Cited by 6 publications

(3 citation statements)

References 16 publications

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“…This setting arises as a special case of our framework. Extensions of filtering on Triplet Markov Trees and pairwise Markov trees are dealt with in Bardel and Desbouvries (2012) and Desbouvries et al (2006) respectively.…”

Section: Related Workmentioning

confidence: 99%

Automatic Backward Filtering Forward Guiding for Markov processes and graphical models

Meulen¹,

Schauer²

2020

Preprint

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We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models. Observations are represented by leaf vertices. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et. al, 2020) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules.The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems,state space models, branching diffusions and Gamma processes.

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Section: Related Workmentioning

confidence: 99%

Automatic Backward Filtering Forward Guiding for Markov processes and graphical models

Meulen¹,

Schauer²

2020

Preprint

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“…Les perspectives pour ce travail contiennent les différentes extensions en complexifiant la loi de ) , , ( Y R U ; en particulier, on peut considérer des processus « partiellement » de Markov, autorisant des bruitages à mémoire longue (Lanchantin et al, 2008 ;Pieczynski, 2013a). On pourra alors envisager d'utiliser ces différents modèles à des fins de lissage ou prédictions, en étendant ainsi les premiers résultats obtenus dans le cadre des ) , , ( Y R X T = dans F , présentés dans (Bardel et Desbouvries, 2012 ;Pieczynski, 2011b). L'estimation des paramètres, en s'inspirant éventuellement de (Fox et al, 2011), constitue une autre perspective intéressante.…”

Section: Filtrage Optimal Avec Sauts 359unclassified

Filtrage statistique optimal rapide dans des systèmes linéaires à sauts non stationnaires

Abbassi

Derrode²,

Desbouvries

et al. 2014

Traitement du signal

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International audienceRESUME. Nous traitons du problème de filtrage statistique optimal dans des systèmes à sauts. Nous considérons trois processus : un processus continu caché X, un processus continu observé Y, et un processus discret caché R modélisant les « sauts », qui peuvent être vus comme les changements aléatoires des paramètres régissant localement les distributions markoviennes du couple (X,Y). Nous nous intéressons à une famille récente de modèles dans laquelle il est possible de mettre en place un filtrage optimal rapide, dont la complexité est linéaire en temps. Nous étendons cette famille en introduisant un quatrième processus discret fini U permettant de modéliser les possibles non-stationnarités du triplet (X, R, Y). Nous montrons que les filtrages optimaux rapides demeurent possibles dans la famille étendue et nous illustrons leur intérêt via quelques simulations. ABSTRACT. This paper deals with optimal statistical filtering in jump systems. We consider three random sequences: a hidden real-valued process X, an observed real-valued process Y and a hidden discrete process R modeling jumps that can be interpreted as random switches in the parameters governing locally the Markovian distributions of the pairwise process (X,Y). We focus on a recent family of models in which it is possible to implement a fast optimal filtering, whose complexity is linear in time. We extend this family by introducing a fourth hidden discrete process U to model possible non-stationarity in triplet (X, R, Y). We show that fast optimal filtering remains possible in the extended family and illustrate their interest via some simulations. MOTS-CLES : Système linéaire gaussien à sauts. Filtrage optimal exact. Modèle caché conditionnellement linéaire à sauts markoviens. Modèle caché conditionnellement linéaire à sauts marginalement markoviens

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“…In addition, different uses of U can be dealt with simultaneously as, for example, in the case of nonstationary hidden semi-Markov model [26]. TMCs have also been used for continuous hidden sequences in Kalman filtering [30], in prediction [31], or still optimal fast filtering in a particular class of switching systems [32]. Finally, let us mention that hidden Markov fields have also been extended to triplet Markov fields [33], and have been successfully applied to complex structure data classification [34], in SAR images processing [35], [36], [37], [38] or biometry [39].…”

Section: Introductionmentioning

confidence: 99%

Phasic Triplet Markov Chains

Boudaren

Monfrini

Pieczynski

et al. 2014

IEEE Trans. Pattern Anal. Mach. Intell.

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Abstract-Hidden Markov chains have been shown to be inadequate for data modeling under some complex conditions. In this work, we address the problem of statistical modeling of phenomena involving two heterogeneous system states. Such phenomena may arise in biology or communications, among other fields. Namely, we consider that a sequence of meaningful words is to be searched within a whole observation that also contains arbitrary one-by-one symbols. Moreover, a word may be interrupted at some site to be carried on later. Applying plain hidden Markov chains to such data, while ignoring their specificity, yields unsatisfactory results. The Phasic triplet Markov chain, proposed in this paper, overcomes this difficulty by means of an auxiliary underlying process in accordance with the triplet Markov chains theory. Related Bayesian restoration techniques and parameters estimation procedures according to the new model are then described. Finally, to assess the performance of the proposed model against the conventional hidden Markov chain model, experiments are conducted on synthetic and real data.

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Exact Bayesian Prediction in a Class of Markov-switching Models

Cited by 6 publications

References 16 publications

Automatic Backward Filtering Forward Guiding for Markov processes and graphical models

Automatic Backward Filtering Forward Guiding for Markov processes and graphical models

Filtrage statistique optimal rapide dans des systèmes linéaires à sauts non stationnaires

Phasic Triplet Markov Chains

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