相关论文: Practical Guide to Monte Carlo

One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…

We introduce a powerful and flexible MCMC algorithm for stochastic simulation. The method builds on a pseudo-marginal method originally introduced in [Genetics 164 (2003) 1139--1160], showing how algorithms which are approximations to an…

We give two direct, elementary proofs that a Monte Carlo simulation converges to equilibrium provided that appropriate conditions are satisfied. The first proof requires detailed balance while the second is quite general.

In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the…

Matrix code allows one to discover algorithms and to render them in code that is both compilable and is correct by construction. In this way the difficulty of verifying existing code is avoided. The method is especially important for…

Markov chain Monte Carlo (MCMC) is a sampling-based method for estimating features of probability distributions. MCMC methods produce a serially correlated, yet representative, sample from the desired distribution. As such it can be…

Monte Carlo methods are now an essential part of the statistician's toolbox, to the point of being more familiar to graduate students than the measure theoretic notions upon which they are based! We recall in this note some of the advances…

Markov Chain Monte Carlo (MCMC) is a computational approach to fundamental problems such as inference, integration, optimization, and simulation. The field has developed a broad spectrum of algorithms, varying in the way they are motivated,…

Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…

In this paper we introduce a new algorithm for American Monte Carlo that can be used either for American-style options, callable structured products or for computing counterparty credit risk (e.g. CVA or PFE computation). Leveraging least…

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…

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…

Differentiable programming has emerged as a key programming paradigm empowering rapid developments of deep learning while its applications to important computational methods such as Monte Carlo remain largely unexplored. Here we present the…

Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…

This is an introductory article about Markov Chain Monte Carlo (MCMC) simulation for pedestrians. Actual simulation codes are provided, and necessary practical details, which are skipped in most textbooks, are shown. The second half is…

We propose a method for Monte Carlo simulations of systems with a complex action. The method has the advantages of being in principle applicable to any such system and provides a solution to the overlap problem. In some cases, like in the…

We propose a novel class of Sequential Monte Carlo (SMC) algorithms, appropriate for inference in probabilistic graphical models. This class of algorithms adopts a divide-and-conquer approach based upon an auxiliary tree-structured…

We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018)), where the manifold is defined by…

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,…

A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…