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We propose Adaptive Incremental Mixture Markov chain Monte Carlo (AIMM), a novel approach to sample from challenging probability distributions defined on a general state-space. While adaptive MCMC methods usually update a parametric…

Methodology · Statistics 2018-06-01 Florian Maire , Nial Friel , Antonietta Mira , Adrian Raftery

This paper introduces a framework for speeding up Bayesian inference conducted in presence of large datasets. We design a Markov chain whose transition kernel uses an (unknown) fraction of (fixed size) of the available data that is randomly…

Methodology · Statistics 2018-06-01 Florian Maire , Nial Friel , Pierre Alquier

We present an original simulation-based method to estimate likelihood ratios efficiently for general state-space models. Our method relies on a novel use of the conditional Sequential Monte Carlo (cSMC) algorithm introduced in…

Methodology · Statistics 2018-09-10 Sinan Yıldırım , Christophe Andrieu , Arnaud Doucet

Adaptive importance sampling (AIS) methods are increasingly used for the approximation of distributions and related intractable integrals in the context of Bayesian inference. Population Monte Carlo (PMC) algorithms are a subclass of AIS…

Computation · Statistics 2022-06-08 Víctor Elvira , Émilie Chouzenoux

In this paper, we address the challenge of Markov Chain Monte Carlo (MCMC) algorithms within the approximate Bayesian Computation (ABC) framework, which often get trapped in local optima due to their inherent local exploration mechanism. We…

Computation · Statistics 2025-12-16 Xuefei Cao , Shijia Wang , Yongdao Zhou

Efficient sampling of many-dimensional and multimodal density functions is a task of great interest in many research fields. We describe an algorithm that allows parallelizing inherently serial Markov chain Monte Carlo (MCMC) sampling by…

Computation · Statistics 2020-08-10 Vasyl Hafych , Philipp Eller , Oliver Schulz , Allen Caldwell

There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable…

Statistics Theory · Mathematics 2021-11-12 Augustin Chevallier , Sam Power , Andi Q. Wang , Paul Fearnhead

Markov Chain Monte Carlo (MCMC) methods sample from unnormalized probability distributions and offer guarantees of exact sampling. However, in the continuous case, unfavorable geometry of the target distribution can greatly limit the…

Machine Learning · Statistics 2020-10-09 Zengyi Li , Yubei Chen , Friedrich T. Sommer

We study the performance of a stochastic algorithm based on the power method that adaptively learns the large deviation functions characterizing the fluctuations of additive functionals of Markov processes, used in physics to model…

Statistical Mechanics · Physics 2023-03-30 Francesco Coghi , Hugo Touchette

In the last two decades, the linear model of coregionalization (LMC) has been widely used to model multivariate spatial processes. However, it can be a challenging task to conduct likelihood-based inference for such models because of the…

Methodology · Statistics 2024-12-04 Renaud Alie , David A. Stephens , Alexandra M. Schmidt

Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…

Computation · Statistics 2021-07-20 Luca Martino , Víctor Elvira

Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…

Probability · Mathematics 2009-10-23 Benjamin Jourdain , Jérôme Lelong

We rely on Monte Carlo (MC) simulations to interpret searches for new physics at the Large Hadron Collider (LHC) and elsewhere. These simulations result in noisy and approximate estimators of selection efficiencies and likelihoods. In this…

High Energy Physics - Phenomenology · Physics 2026-04-22 Christopher Chang , Benjamin Farmer , Andrew Fowlie , Anders Kvellestad

Accept-reject based Markov chain Monte Carlo (MCMC) algorithms have traditionally utilised acceptance probabilities that can be explicitly written as a function of the ratio of the target density at the two contested points. This feature is…

Computation · Statistics 2021-04-26 Dootika Vats , Flávio Gonçalves , Krzysztof Łatuszyński , Gareth O. Roberts

The efficiency of a Markov chain Monte Carlo algorithm might be measured by the cost of generating one independent sample, or equivalently, the total cost divided by the effective sample size, defined in terms of the integrated…

Computation · Statistics 2017-05-12 Youhan Fang , Yudong Cao , Robert D. Skeel

In this work we propose a hierarchy of Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub - steps…

Numerical Analysis · Mathematics 2015-05-30 Evangelia Kalligiannaki , Markos A. Katsoulakis , Petr Plechac , Dionisios G Vlachos

In this article we propose a novel MCMC method based on deterministic transformations T: X x D --> X where X is the state-space and D is some set which may or may not be a subset of X. We refer to our new methodology as Transformation-based…

Computation · Statistics 2013-10-21 Somak Dutta , Sourabh Bhattacharya

Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics…

Numerical Analysis · Mathematics 2025-02-13 Geoffrey McGregor , Andy T. S. Wan

As it has become common to use many computer cores in routine applications, finding good ways to parallelize popular algorithms has become increasingly important. In this paper, we present a parallelization scheme for Markov chain Monte…

Methodology · Statistics 2016-06-01 Guillaume W. Basse , Natesh S. Pillai , Aaron Smith

Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud…