Related papers: Metropolis Monte Carlo sampling: convergence, loca…

We connect known results about diffusion limits of Markov chain Monte Carlo (MCMC) algorithms to the Computer Science notion of algorithm complexity. Our main result states that any diffusion limit of a Markov process implies a…

In dynamic Monte Carlo simulations, using for example the Metropolis dynamic, it is often required to simulate for long times and to simulate large systems. We present an overview of advanced algorithms to simulate for larger times and to…

We study the integration of functions with respect to an unknown density. We compare the simple Monte Carlo method (which is almost optimal for a certain large class of inputs) and compare it with the Metropolis algorithm (based on a…

We propose an adaptive Metropolis-Hastings algorithm in which sampled data are used to update the proposal distribution. We use the samples found by the algorithm at a particular step to form the information-theoretically optimal mean-field…

Convergence analysis of Markov chain Monte Carlo methods in high-dimensional statistical applications is increasingly recognized. In this paper, we develop general mixing time bounds for Metropolis-Hastings algorithms on discrete spaces by…

Both resources in the natural environment and concepts in a semantic space are distributed "patchily", with large gaps in between the patches. To describe people's internal and external foraging behavior, various random walk models have…

We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We…

We propose an efficient Markov Chain Monte Carlo method for sampling equilibrium distributions for stochastic lattice models, capable of handling correctly long and short-range particle interactions. The proposed method is a Metropolis-type…

We propose a new sampling algorithm combining two quite powerful ideas in the Markov chain Monte Carlo literature -- adaptive Metropolis sampler and two-stage Metropolis-Hastings sampler. The proposed sampling method will be particularly…

It has become increasingly easy nowadays to collect approximate posterior samples via fast algorithms such as variational Bayes, but concerns exist about the estimation accuracy. It is tempting to build solutions that exploit approximate…

We discuss several algorithms for sampling from unnormalized probability distributions in statistical physics, but using the language of statistics and machine learning. We provide a self-contained introduction to some key ideas and…

We discuss non-reversible Markov-chain Monte Carlo algorithms that, for particle systems, rigorously sample the positional Boltzmann distribution and that have faster than physical dynamics. These algorithms all feature a non-thermal…

We consider the optimal scaling problem for high-dimensional random walk Metropolis (RWM) algorithms where the target distribution has a discontinuous probability density function. Almost all previous analysis has focused upon continuous…

We consider versions of the Metropolis algorithm which avoid the inefficiency of rejections. We first illustrate that a natural Uniform Selection Algorithm might not converge to the correct distribution. We then analyse the use of Markov…

Monte Carlo methods play an important role in scientific computation, especially when problems have a vast phase space. In this lecture an introduction to the Monte Carlo method is given. Concepts such as Markov chains, detailed balance,…

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…

High-dimensional distributions, especially those with heavy tails, are notoriously difficult for off-the-shelf MCMC samplers: the combination of unbounded state spaces, diminishing gradient information, and local moves results in…

Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…

We study the large-scale dynamics of event chain Monte Carlo algorithms in one dimension, and their relation to the true self-avoiding walk. In particular, we study the influence of stress, and different forms of interaction on the…

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…