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Markov jump processes are continuous-time stochastic processes which describe dynamical systems evolving in discrete state spaces. These processes find wide application in the natural sciences and machine learning, but their inference is…

We consider the analysis of sets of categorical sequences consisting of piecewise homogeneous Markov segments. The sequences are assumed to be governed by a common underlying process with segments occurring in the same order for each…

We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities,…

Compared to the nominal scale, the ordinal scale for a categorical outcome variable has the property of making a monotonicity assumption for the covariate effects meaningful. This assumption is encoded in the commonly used proportional odds…

Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…

This paper presents a numerical method to calculate the value function for a general discounted impulse control problem for piecewise deterministic Markov processes. Our approach is based on a quantization technique for the underlying…

Among random sampling methods, Markov Chain Monte Carlo algorithms are foremost. Using a combination of analytical and numerical approaches, we study their convergence properties towards the steady state, within a random walk Metropolis…

We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The…

Piecewise Deterministic Markov Processes (PDMPs) such as the Bouncy Particle Sampler and the Zig-Zag Sampler, have gained attention as continuous-time counterparts of classical Markov chain Monte Carlo. We study their transient regime under…

We consider chemical reaction networks modeled by a discrete state and continuous in time Markov process for the vector copy number of the species and provide a novel particle filter method for state and parameter estimation based on exact…

We introduce a new multivariate circular linear distribution suitable for modeling direction and speed in (multiple) animal movement data. To properly account for specific data features, such as heterogeneity and time dependence, a hidden…

A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…

Jump Markov linear models consists of a finite number of linear state space models and a discrete variable encoding the jumps (or switches) between the different linear models. Identifying jump Markov linear models makes for a challenging…

Jump Markov linear systems (JMLS) are a useful class which can be used to model processes which exhibit random changes in behavior during operation. This paper presents a numerically stable method for learning the parameters of jump Markov…

We propose a unified framework that employs variational inference (VI) with (conditional) normalizing flows (NFs) to train both between-model and within-model proposals for reversible jump Markov chain Monte Carlo, enabling efficient…

Markov jump processes (MJPs) are continuous-time stochastic processes widely used in a variety of applied disciplines. Inference for MJPs typically proceeds via Markov chain Monte Carlo, the state-of-the-art being a uniformization-based…

We study continuous time Markov processes on graphs. The notion of frequency is introduced, which serves well as a scaling factor between any Markov time of a continuous time Markov process and that of its jump chain. As an application, we…

Full Bayesian computational inference for model determination in undirected graphical models is currently restricted to decomposable graphs, except for problems of very small scale. In this paper we develop new, more efficient methodology…

This paper considers the problem of remote state estimation for Markov jump linear systems in the presence of uncertainty in the posterior mode probabilities. Such uncertainty may arise when the estimator receives noisy or incomplete…

We develop a variational Bayesian (VB) approach for estimating large-scale dynamic network models in the network autoregression framework. The VB approach allows for the automatic identification of the dynamic structure of such a model and…