A class of fast exact Bayesian filters in dynamical models with jumps

In this paper, we focus on the statistical filtering problem in dynamical models with jumps. When a particular application relies on physical properties which are modeled by linear and Gaussian probability density functions with jumps, an usualmethod consists in approximating the optimal Bayesian estimate (in the sense of the Minimum Mean Square Error (MMSE)) in a linear and Gaussian Jump Markov State Space System (JMSS). Practical solutions include algorithms based on numerical approximations or based on Sequential Monte Carlo (SMC) methods. In this paper, we propose a class of alternative methods which consists in building statistical models which share the same physical properties of interest but in which the computation of the optimal MMSE estimate can be done at a computational cost which is linear in the number of observations.Comment: 21 pages, 7 figure

Statistical Inference for Partially Observed Markov Processes via the R Package pomp

Partially observed Markov process (POMP) models, also known as hidden Markov models or state space models, are ubiquitous tools for time series analysis. The R package pomp provides a very flexible framework for Monte Carlo statistical investigations using nonlinear, non-Gaussian POMP models. A range of modern statistical methods for POMP models have been implemented in this framework including sequential Monte Carlo, iterated filtering, particle Markov chain Monte Carlo, approximate Bayesian computation, maximum synthetic likelihood estimation, nonlinear forecasting, and trajectory matching. In this paper, we demonstrate the application of these methodologies using some simple toy problems. We also illustrate the specification of more complex POMP models, using a nonlinear epidemiological model with a discrete population, seasonality, and extra-demographic stochasticity. We discuss the specification of user-defined models and the development of additional methods within the programming environment provided by pomp.Comment: In press at the Journal of Statistical Software. A version of this paper is provided at the pomp package website: http://kingaa.github.io/pom

Latent parameter estimation in fusion networks using separable likelihoods

Multi-sensor state space models underpin fusion applications in networks of sensors. Estimation of latent parameters in these models has the potential to provide highly desirable capabilities such as network self-calibration. Conventional solutions to the problem pose difficulties in scaling with the number of sensors due to the joint multi-sensor filtering involved when evaluating the parameter likelihood. In this article, we propose a separable pseudo-likelihood which is a more accurate approximation compared to a previously proposed alternative under typical operating conditions. In addition, we consider using separable likelihoods in the presence of many objects and ambiguity in associating measurements with objects that originated them. To this end, we use a state space model with a hypothesis based parameterisation, and, develop an empirical Bayesian perspective in order to evaluate separable likelihoods on this model using local filtering. Bayesian inference with this likelihood is carried out using belief propagation on the associated pairwise Markov random field. We specify a particle algorithm for latent parameter estimation in a linear Gaussian state space model and demonstrate its efficacy for network self-calibration using measurements from non-cooperative targets in comparison with alternatives.Comment: accepted with minor revisions, IEEE Transactions on Signal and Information Processing Over Network

Connected image processing with multivariate attributes: an unsupervised Markovian classification approach

International audienceThis article presents a new approach for constructing connected operators for image processing and analysis. It relies on a hierarchical Markovian unsupervised algorithm in order to classify the nodes of the traditional Max-Tree. This approach enables to naturally handle multivariate attributes in a robust non-local way. The technique is demonstrated on several image analysis tasks: filtering, segmentation, and source detection, on astronomical and biomedical images. The obtained results show that the method is competitive despite its general formulation. This article provides also a new insight in the field of hierarchical Markovian image processing showing that morphological trees can advantageously replace traditional quadtrees