Fast exact filtering in generalized conditionally observed Markov switching models with copulas

International audienceWe deal with the problem of statistical filtering in the context of Markov switching models. For X_1^N hidden continuous process, R_1^N hidden finite Markov process, and Y_1^N observed continuous one, the problem is to sequentially estimate X_1^N and R_1^N from Y_1^N. In the classical " conditional Gaussian Linear state space model " (CGLSSM), where (R_1^N, X_1^N) is a hidden Gaussian Markov chain, fast exact filtering is not workable. Recently, " conditionally Gaussian observed Markov switching model " (CGOMSM) has been proposed, in which (R_1^N, Y_1^N) is a hidden Gaussian Markov chain instead. This model allows fast exact filtering. In this paper, using copula, we extend CGOMSM to a more general one, in which (R_1^N, Y_1^N) is a hidden Markov chain (HMC) with noise of any form and the regimes are no need to be all Gaussian, while the exact filtering is still workable. Experiments are conducted to show how the exact filtering results based on CGOMSM can be improved by the use of the new model

Unsupervised classification using hidden Markov chain with unknown noise copulas and margins

International audienceWe consider the problem of unsupervised classification of hidden Markov models (HMC) with dependent noise. Time is discrete, the hidden process takes its values in a finite set of classes, while the observed process is continuous. We adopt an extended HMC model in which the rich possibilities of different kinds of dependence in the noise are modelled via copulas. A general model identification algorithm, in which different noise margins and copulas corresponding to different classes are selected in given families and estimated in an automated way, from the sole observed process, is proposed. The interest of the whole procedure is shown via experiments on simulated data and on a real SAR image

Unsupervised classification using hidden Markov chain with unknown noise copulas and margins

International audienceWe consider the problem of unsupervised classification of hidden Markov models (HMC) with dependent noise. Time is discrete, the hidden process takes its values in a finite set of classes, while the observed process is continuous. We adopt an extended HMC model in which the rich possibilities of different kinds of dependence in the noise are modelled via copulas. A general model identification algorithm, in which different noise margins and copulas corresponding to different classes are selected in given families and estimated in an automated way, from the sole observed process, is proposed. The interest of the whole procedure is shown via experiments on simulated data and on a real SAR image