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We propose a sampling algorithm to perform system identification from a set of input-output graph signal pairs. The dynamics of the systems we study are given by a partially known adjacency matrix and a generic parametric graph filter of…
The Ensemble Score Filter (EnSF) has emerged as a promising approach to leverage score-based diffusion models for solving high-dimensional and nonlinear data assimilation problems. While initial applications of EnSF to the Lorenz-96 model…
Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal density. The mixture model can be…
Multi-state models are commonly used for intermittent observations of a state over time, but these are generally based on the Markov assumption, that transition rates are independent of the time spent in current and previous states. In a…
The state estimation problem for nonlinear systems with stochastic uncertainties can be formulated in the Bayesian framework, where the objective is to replace the state completely by its probability density function. Without the…
We propose a Bayesian inference approach for a class of latent Markov models. These models are widely used for the analysis of longitudinal categorical data, when the interest is in studying the evolution of an individual unobservable…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
Integrating heterogeneous data sources and expert knowledge is essential for overcoming data scarcity and enhancing estimation accuracy. Two main frameworks naturally arise to perform the integration of these multiple sources: sequential…
The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors…
A generic algorithm for the extraction of probabilistic (Bayesian) information about model parameters from data is presented. The algorithm propagates an ensemble of particles in the product space of model parameters and outputs. Each…
We present a general form of the iteration and interpolation process used in implicit particle filters. Implicit filters are based on a pseudo-Gaussian representation of posterior densities, and are designed to focus the particle paths so…
The aim of this chapter is twofold. In the first part we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures.…
Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The…
Ensemble forecasting of nonlinear systems involves the use of a model to run forward a discrete ensemble (or set) of initial states. Data assimilation techniques tend to focus on estimating the true state of the system, even though model…
This paper explores the versatility and depth of Bayesian modeling by presenting a comprehensive range of applications and methods, combining Markov chain Monte Carlo (MCMC) techniques and variational approximations. Covering topics such as…
Data assimilation is a technique for increasing the accuracy of simulations of solutions to partial differential equations by incorporating observable data into the solution as time evolves. Recently, a promising new algorithm for data…
The Markov modulated (switching) state space is an important model paradigm in applied statistics. In this article, we specifically consider Markov modulated nonlinear state-space models and address the online Bayesian inference problem for…
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…
Exact inference for hidden Markov models requires the evaluation of all distributions of interest - filtering, prediction, smoothing and likelihood - with a finite computational effort. This article provides sufficient conditions for exact…
Clustering has become a core technology in machine learning, largely due to its application in the field of unsupervised learning, clustering, classification, and density estimation. A frequentist approach exists to hand clustering based on…