Related papers: Transient regime of piecewise deterministic Monte …

Markov chain Monte Carlo methods are central in computational statistics, and typically rely on detailed balance to ensure invariance with respect to a target distribution. Although straightforward to construct by Metropolization, this can…

We propose Parallelised Diffeomorphic Sampling-based Motion Planning (PDMP). PDMP is a novel parallelised framework that uses bijective and differentiable mappings, or diffeomorphisms, to transform sampling distributions of sampling-based…

We propose a numerical method to approximate the value function for the optimal stopping problem of a piecewise deterministic Markov process (PDMP). Our approach is based on quantization of the post jump location---inter-arrival time Markov…

The velocity-jump model is a specific type of piecewise deterministic Markov process in which an individual's velocity is constant except at times that form the events of some point process. It represents an interpretable continuous-time…

The persistent walk is a classical model in kinetic theory, which has also been studied as a toy model for MCMC questions. Its continuous limit, the telegraph process, has recently been extended to various velocity jump processes (Bouncy…

Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking…

Constrained Markov decision processes (CMDPs) are used as a decision-making framework to study the long-run performance of a stochastic system. It is well-known that a stationary optimal policy of a CMDP problem under discounted cost…

The need to calibrate increasingly complex statistical models requires a persistent effort for further advances on available, computationally intensive Monte Carlo methods. We study here an advanced version of familiar Markov Chain Monte…

We discuss a non-reversible, lifted Markov-chain Monte Carlo (MCMC) algorithm for particle systems in which the direction of proposed displacements is changed deterministically. This algorithm sweeps through directions analogously to the…

This paper proposes a new sampling scheme based on Langevin dynamics that is applicable within pseudo-marginal and particle Markov chain Monte Carlo algorithms. We investigate this algorithm's theoretical properties under standard…

Designing efficient and rigorous numerical methods for sequential decision-making under uncertainty is a difficult problem that arises in many applications frameworks. In this paper we focus on the numerical solution of a subclass of…

New sampling algorithms based on simulating continuous-time stochastic processes called piece-wise deterministic Markov processes (PDMPs) have shown considerable promise. However, these methods can struggle to sample from multi-modal or…

The Direct Simulation Monte Carlo (DSMC) method is widely employed for simulating rarefied nonequilibrium gas flows. With advances in aerospace engineering and micro/nano-scale technologies, gas flows exhibit the coexistence of rarefied and…

We study the rate of convergence to equilibrium of the self-repellent random walk and its local time process on the discrete circle $\mathbb{Z}_n$. While the self-repellent random walk alone is non-Markovian since the jump rates depend on…

Event-Chain Monte Carlo (ECMC) methods generate continuous-time and non-reversible Markov processes which often display significant accelerations compared to reversible counterparts. However their generalization to any system may appear…

Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…

The Hamiltonian Monte Carlo (HMC) sampling algorithm exploits Hamiltonian dynamics to construct efficient Markov Chain Monte Carlo (MCMC), which has become increasingly popular in machine learning and statistics. Since HMC uses the gradient…

In terms of the stochastic process of quantum-mechanical version of Markov chain Monte Carlo method (the MCMC), we analytically derive macroscopically deterministic flow equations of order parameters such as spontaneous magnetization in…

We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete…

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has become increasingly popular for simulating posterior samples in large-scale Bayesian modeling. However, existing SG-MCMC schemes are not tailored to any specific probabilistic…