Related papers: Parallelization of adaptive MC Integrators

Parallel tempering is a generic Markov chain Monte Carlo sampling method which allows good mixing with multimodal target distributions, where conventional Metropolis-Hastings algorithms often fail. The mixing properties of the sampler…

We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov Chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on…

Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has…

Massively parallel desktop computing capabilities now well within the reach of individual academics modify the environment for posterior simulation in fundamental and potentially quite advantageous ways. But to fully exploit these benefits…

In this paper we study the ergodicity properties of some adaptive Markov chain Monte Carlo algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated…

A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as…

We present an extension of the semi-grandcanonical (SGC) ensemble that we refer to as the variance-constrained semi-grandcanonical (VC-SGC) ensemble. It allows for transmutation Monte Carlo simulations of multicomponent systems in…

Performing exact Bayesian inference for complex models is computationally intractable. Markov chain Monte Carlo (MCMC) algorithms can provide reliable approximations of the posterior distribution but are expensive for large datasets and…

We propose a novel hybrid quantum computing strategy for parallel MCMC algorithms that generate multiple proposals at each step. This strategy makes the rate-limiting step within parallel MCMC amenable to quantum parallelization by using…

Parallel tempering is a meta-algorithm for Markov Chain Monte Carlo that uses multiple chains to sample from tempered versions of the target distribution, enhancing mixing in multi-modal distributions that are challenging for traditional…

Sequential Monte Carlo samplers represent a compelling approach to posterior inference in Bayesian models, due to being parallelisable and providing an unbiased estimate of the posterior normalising constant. In this work, we significantly…

Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…

It is well known that Monte Carlo integration with variance reduction by means of control variates can be implemented by the ordinary least squares estimator for the intercept in a multiple linear regression model. A central limit theorem…

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…

Monte Carlo methods -- such as Markov chain Monte Carlo (MCMC) and piecewise deterministic Markov process (PDMP) samplers -- provide asymptotically exact estimators of expectations under a target distribution. There is growing interest in…

There has been a recent surge of interest in coupling methods for Markov chain Monte Carlo algorithms: they facilitate convergence quantification and unbiased estimation, while exploiting embarrassingly parallel computing capabilities.…

Markov chain Monte Carlo (MCMC) is the predominant tool used in Bayesian parameter estimation for hierarchical models. When the model expands due to an increasing number of hierarchical levels, number of groups at a particular level, or…

We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy…

Performing numerical integration when the integrand itself cannot be evaluated point-wise is a challenging task that arises in statistical analysis, notably in Bayesian inference for models with intractable likelihood functions. Markov…

Gibbs sampling is a widely used Markov chain Monte Carlo (MCMC) method for numerically approximating integrals of interest in Bayesian statistics and other mathematical sciences. Many implementations of MCMC methods do not extend easily to…