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Markov chain Monte Carlo methods are a powerful tool for sampling equilibrium configurations in complex systems. One problem these methods often face is slow convergence over large energy barriers. In this work, we propose a novel method…

Most Markov chain Monte Carlo methods operate in discrete time and are reversible with respect to the target probability. Nevertheless, it is now understood that the use of non-reversible Markov chains can be beneficial in many contexts. In…

Szegedy's quantization of a reversible Markov chain provides a quantum walk whose spectral gap is quadratically larger than that of the classical walk. Quantum computers are therefore expected to provide a speedup of Metropolis-Hastings…

We introduced the Hug and Hop Markov chain Monte Carlo algorithm for estimating expectations with respect to an intractable distribution. The algorithm alternates between two kernels: Hug and Hop. Hug is a non-reversible kernel that…

In this paper we present an extension of population-based Markov chain Monte Carlo (MCMC) to the trans-dimensional case. One of the main challenges in MCMC-based inference is that of simulating from high and trans-dimensional target…

We propose a new method for Monte Carlo solution of non-linear integral equations by combining the Newton-Kantorovich method for solving non-linear equations with the Markov Chain Monte Carlo (MCMC) method for solving linear equations. The…

Quantum-enhanced Markov chain Monte Carlo, an algorithm in which configurations are proposed through a measured quantum quench and accepted or rejected by a classical algorithm, has been proposed as a possible method for robust quantum…

We present an extension of the corner transfer matrix renormalisation group (CTMRG) method to O(n) invariant models, with particular interest in the self-avoiding walk class of models (O(n=0)). The method is illustrated using an interacting…

We examine self-avoiding walks in dimensions 4 to 8 using high-precision Monte-Carlo simulations up to length N=16384, providing the first such results in dimensions $d > 4$ on which we concentrate our analysis. We analyse the scaling…

Markov chains based on spanning trees have been hugely influential in algorithms for assessing fairness in political redistricting. The input graph represents the geographic building blocks of a jurisdiction. The goal is to output a large…

Random Walk Metropolis Hastings (RWMH) algorithm, is quite inefficient in high dimensions because of its abysmally slow acceptance rate. The slow acceptance rate results from the fact that RWMH separately updates each coordinate of the…

Practitioners of Markov chain Monte Carlo (MCMC) may hesitate to use random walk Metropolis-Hastings algorithms, especially variable-at-a-time algorithms with many parameters, because these algorithms require users to select values of…

Markov Chain Monte Carlo inference of target posterior distributions in machine learning is predominately conducted via Hamiltonian Monte Carlo and its variants. This is due to Hamiltonian Monte Carlo based samplers ability to suppress…

Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential…

This article was motivated by the desire to improve Markov chain Monte Carlo methods for spatial survival models in which the locations of individuals in space are known. For a dataset comprising information on n individuals, standard…

Markov Chain Monte Carlo algorithms, the method of choice to sample from generic high-dimensional distributions, are rarely used for continuous one-dimensional distributions, for which more effective approaches are usually available (e.g.…

We study terminally attached self-avoiding walks and bridges on the simple cubic lattice, both by series analysis and Monte Carlo methods. We provide strong numerical evidence supporting a scaling relation between self-avoiding walks,…

Novel Markov Chain Monte Carlo (MCMC) methods have enabled the generation of large ensembles of redistricting plans through graph partitioning. However, existing algorithms such as Reversible Recombination (RevReCom) and Metropolized Forest…

In this paper we build on previous work which uses inferences techniques, in particular Markov Chain Monte Carlo (MCMC) methods, to solve parameterized control problems. We propose a number of modifications in order to make this approach…

Evaluating the degree of partisan districting (Gerrymandering) in a statistical framework typically requires an ensemble of districting plans which are drawn from a prescribed probability distribution that adheres to a realistic and…