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Continuous-time multistate models are widely used for analyzing interval-censored data on disease progression over time. Sometimes, diseases manifest differently and what appears to be a coherent collection of symptoms is the expression of…

Piecewise-deterministic Markov processes (PDMPs) are often used to model abrupt changes in the global environment or capabilities of a controlled system. This is typically done by considering a set of "operating modes" (each with its own…

Active classification, i.e., the sequential decision-making process aimed at data acquisition for classification purposes, arises naturally in many applications, including medical diagnosis, intrusion detection, and object tracking. In this…

Stochastic epidemic models provide an interpretable probabilistic description of the spread of a disease through a population. Yet, fitting these models to partially observed data is a notoriously difficult task due to intractability of the…

This paper deals with control of partially observable discrete-time stochastic systems. It introduces and studies Markov Decision Processes with Incomplete Information and with semi-uniform Feller transition probabilities. The important…

This document is the Part IV of the book 'Stochastic Epidemic Models with Inference' edited by Tom Britton and Etienne Pardoux. It is written by Catherine Lar\'edo, with the contribution of Viet Chi Tran for the Chapter 4. Epidemic data…

Parameter inference and state estimation in stochastic and partially observed biological systems remain major problems in mathematical biology. In this work, we introduce a two-dimensional lattice graph model for the spread of infectious…

Markovian population models are suitable abstractions to describe well-mixed interacting particle systems in situation where stochastic fluctuations are significant due to the involvement of low copy particles. In molecular biology,…

Random walks on networks is the standard tool for modelling spreading processes in social and biological systems. This first-order Markov approach is used in conventional community detection, ranking, and spreading analysis although it…

The early detection of infectious disease outbreaks is a crucial task to protect population health. To this end, public health surveillance systems have been established to systematically collect and analyse infectious disease data. A…

Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…

We propose a causal hidden Markov model to achieve robust prediction of irreversible disease at an early stage, which is safety-critical and vital for medical treatment in early stages. Specifically, we introduce the hidden variables which…

Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which…

Compartmental epidemic models have been widely used for predicting the course of epidemics, from estimating the basic reproduction number to guiding intervention policies. Studies commonly acknowledge these models' assumptions but less…

Partially Observable Markov Decision Processes (POMDPs) model decision making under uncertainty. While there are many approaches to approximately solving POMDPs, we aim to address the problem of learning such models. In particular, we are…

The influence model is a discrete-time stochastic model that succinctly captures the interactions of a network of Markov chains. The model produces a reduced-order representation of the stochastic network, and can be used to describe and…

Global pandemics, such as the recent COVID-19 crisis, highlight the need for stochastic epidemic models that can capture the randomness inherent in the spread of disease. Such models must be accompanied by methods for estimating parameters…

We present a new Bayesian inference method for compartmental models that takes into account the intrinsic stochasticity of the process. We show how to formulate a SIR-type Markov jump process as the solution of a stochastic differential…

We investigate partially observed Markov decision processes (POMDPs) with cost functions regularized by entropy terms describing state, observation, and control uncertainty. Standard POMDP techniques are shown to offer bounded-error…

In this paper, we consider a discrete-time stochastic SIR model, where the transmission rate and the true number of infectious individuals are random and unobservable. An advantage of this model is that it permits us to account for random…