Related papers: A Spectrum of Approximate Probabilistic Bisimulati…

The paper is concerned with approximating the distribution of a sum W of n integer valued random variables Y_i, whose distributions depend on the state of an underlying Markov chain X. The approximation is in terms of a translated Poisson…

Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…

In a first part, we prove Bernstein-type deviation inequalities for bifurcating Markov chains (BMC) under a geometric ergodicity assumption, completing former results of Guyon and Bitseki Penda, Djellout and Guillin. These preliminary…

Computing the marginal likelihood or evidence is one of the core challenges in Bayesian analysis. While there are many established methods for estimating this quantity, they predominantly rely on using a large number of posterior samples…

In this paper we consider Markov chains with transition rates that depend on a small parameter $\varepsilon$. Under a mild assumption on the asymptotics of these transition rates, we describe the behavior of the chain at various…

Bisimulation metrics provide a robust and accurate approach to study the behavior of nondeterministic probabilistic processes. In this paper, we propose a logical characterization of bisimulation metrics based on a simple probabilistic…

This paper presents a Markov chain Monte Carlo method to generate approximate posterior samples in retrospective multiple changepoint problems where the number of changes is not known in advance. The method uses conjugate models whereby the…

This article presents a Bayesian inferential method where the likelihood for a model is unknown but where data can easily be simulated from the model. We discretize simulated (continuous) data to estimate the implicit likelihood in a…

A large number of statistical models are "doubly-intractable": the likelihood normalising term, which is a function of the model parameters, is intractable, as well as the marginal likelihood (model evidence). This means that standard…

This paper advocates proximal Markov Chain Monte Carlo (ProxMCMC) as a flexible and general Bayesian inference framework for constrained or regularized estimation. Originally introduced in the Bayesian imaging literature, ProxMCMC employs…

We develop a framework for the compression of reversible Markov chains with rigorous error control. Given a subset of selected states, we construct reduced dynamics that can be lifted to an approximation of the full dynamics, and we prove…

We are interested in studying the sensitivity of diffusion processes or their approximations by Markov Chains with respect to a perturbation of the coefficients.

Reversibility is a key property of Markov chains, central to algorithms such as Metropolis-Hastings and other MCMC methods. Yet many applications yield non-reversible chains, motivating the problem of approximating them by reversible ones…

This paper is concerned with the development of rigorous approximations to various expectations associated with Markov chains and processes having non-stationary transition probabilities. Such non-stationary models arise naturally in…

Monte Carlo algorithms often aim to draw from a distribution $\pi$ by simulating a Markov chain with transition kernel $P$ such that $\pi$ is invariant under $P$. However, there are many situations for which it is impractical or impossible…

We propose new Markov Chain Monte Carlo algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of set-valued maps in the proposal step of the MCMC algorithms. The motivation for…

We investigate how various forms of bisimulation can be characterised using the technology of logical relations. The approach taken is that each form of bisimulation corresponds to an algebraic structure derived from a transition system,…

Approximate Bayesian computation (ABC) is a popular technique for approximating likelihoods and is often used in parameter estimation when the likelihood functions are analytically intractable. Although the use of ABC is widespread in many…

Finite mixture models are used in statistics and other disciplines, but inference for mixture models is challenging due, in part, to the multimodality of the likelihood function and the so-called label switching problem. We propose…

Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a…