Related papers: Metropolis Sampling
Hamiltonian Monte Carlo (HMC) is a popular Markov chain Monte Carlo (MCMC) algorithm that generates proposals for a Metropolis-Hastings algorithm by simulating the dynamics of a Hamiltonian system. However, HMC is sensitive to large time…
Sampling from high dimensional distributions is a computational bottleneck in many scientific applications. Hamiltonian Monte Carlo (HMC), and in particular the No-U-Turn Sampler (NUTS), are widely used, yet they struggle on problems with a…
Markov Chain Monte Carlo (MCMC) algorithms are widely used for stochastic optimization, sampling, and integration of mathematical objective functions, in particular, in the context of Bayesian inverse problems and parameter estimation. For…
The problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Monte Carlo Markov Chain (MCMC) sampling methods have been adapted to handle different types of…
We introduce a modification of the well-known Metropolis importance sampling algorithm by using a methodology inspired on the consideration of the reparametrization invariance of the microcanonical ensemble. The most important feature of…
Markov chain Monte Carlo (MCMC) methods are widely used in machine learning. One of the major problems with MCMC is the question of how to design chains that mix fast over the whole state space; in particular, how to select the parameters…
We discuss modern ideas in Monte Carlo algorithms in the simplified setting of the one-dimensional anharmonic oscillator. After reviewing the connection between molecular dynamics and Monte Carlo, we introduce to the Metropolis and the…
Markov Chain Monte Carlo (MCMC) is a class of algorithms to sample complex and high-dimensional probability distributions. The Metropolis-Hastings (MH) algorithm, the workhorse of MCMC, provides a simple recipe to construct reversible…
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…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC) algorithm for estimating expectations with respect to continuous un-normalized probability distributions. MCMC estimators typically have higher variance than…
Motivated by the physics of strings and branes, we develop a class of Markov chain Monte Carlo (MCMC) algorithms involving extended objects. Starting from a collection of parallel Metropolis-Hastings (MH) samplers, we place them on an…
Markov chain Monte Carlo (MCMC) methods have existed for a long time and the field is well-explored. The purpose of MCMC methods is to approximate a distribution through repeated sampling; most MCMC algorithms exhibit asymptotically optimal…
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,…
Markov Chain Monte Carlo (MCMC) sampling methods are widely used but often encounter either slow convergence or biased sampling when applied to multimodal high dimensional distributions. In this paper, we present a general framework of…
Markov chain Monte Carlo (MCMC) sampling is an important and commonly used tool for the analysis of hierarchical models. Nevertheless, practitioners generally have two options for MCMC: utilize existing software that generates a black-box…
Particle Markov Chain Monte Carlo (PMCMC) is a general computational approach to Bayesian inference for general state space models. Our article scales up PMCMC in terms of the number of observations and parameters by generating the…
Bayesian inference via standard Markov Chain Monte Carlo (MCMC) methods is too computationally intensive to handle large datasets, since the cost per step usually scales like $\Theta(n)$ in the number of data points $n$. We propose the…
Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many-body systems. This paper will consider some of the generalizations of…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…