Related papers: Efficient Computation of Updated Lower Expectation…

We propose a unified framework that extends the inference methods for classical hidden Markov models to continuous settings, where both the hidden states and observations occur in continuous time. Two different settings are analyzed: hidden…

The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…

Systems of interacting continuous-time Markov chains are a powerful model class, but inference is typically intractable in high dimensional settings. Auxiliary information, such as noisy observations, is typically only available at discrete…

The theory of imprecise Markov chains has achieved significant progress in recent years. Its applicability, however, is still very much limited, due in large part to the lack of efficient computational methods for calculating…

We consider the filtering of continuous-time finite-state hidden Markov models, where the rate and observation matrices depend on unknown time-dependent parameters, for which no prior or stochastic model is available. We quantify and…

This report addresses state inference for hidden Markov models. These models rely on unobserved states, which often have a meaningful interpretation. This makes it necessary to develop diagnostic tools for quantification of state…

Even simply-defined, finite-state generators produce stochastic processes that require tracking an uncountable infinity of probabilistic features for optimal prediction. For processes generated by hidden Markov chains the consequences are…

Marginal expected shortfall is unquestionably one of the most popular systemic risk measures. Studying its extreme behaviour is particularly relevant for risk protection against severe global financial market downturns. In this context,…

There is a lack of methodological results for continuous time change detection due to the challenges of noninformative prior specification and efficient posterior inference in this setting. Most methodologies to date assume data are…

Herein, the Hidden Markov Model is expanded to allow for Markov chain observations. In particular, the observations are assumed to be a Markov chain whose one step transition probabilities depend upon the hidden Markov chain. An…

We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now…

Hidden Markov models (HMMs) are probabilistic functions of finite Markov chains, or, put in other words, state space models with finite state space. In this paper, we examine subspace estimation methods for HMMs whose output lies a finite…

We present a numerical method to compute expectations of functionals of a piecewise-deterministic Markov process. We discuss time dependent functionals as well as deterministic time horizon problems. Our approach is based on the…

Reversible Markov chains play a central role in stochastic modelling and in algorithms such as Markov chain Monte Carlo (MCMC). Motivated by the fundamental importance of reversibility in classical settings, this paper develops a…

This paper studies the estimation of low-rank Markov chains from empirical trajectories. We propose a non-convex estimator based on rank-constrained likelihood maximization. Statistical upper bounds are provided for the Kullback-Leiber…

In this paper, selection of an active sensor subset for tracking a discrete time, finite state Markov chain having an unknown transition probability matrix (TPM) is considered. A total of N sensors are available for making observations of…

Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…

Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously…

Given noisy, partial observations of a time-homogeneous, finite-statespace Markov chain, conceptually simple, direct statistical inference is available, in theory, via its rate matrix, or infinitesimal generator, $\mathsf{Q}$, since $\exp…

Latent position models are widely used for the analysis of networks in a variety of research fields. In fact, these models possess a number of desirable theoretical properties, and are particularly easy to interpret. However, statistical…