相关论文: Discussions on "Riemann manifold Langevin and Hami…

This technical report is the union of two contributions to the discussion of the Read Paper "Riemann manifold Langevin and Hamiltonian Monte Carlo methods" by B. Calderhead and M. Girolami, presented in front of the Royal Statistical…

The paper proposes a Riemannian Manifold Hamiltonian Monte Carlo sampler to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The…

This is the compilation of our comments submitted to the Journal of the Royal Statistical Society, Series B, to be published within the discussion of the Read Paper of Andrieu, Doucet and Hollenstein.

Markov Chain Monte Carlo (MCMC) is an invaluable means of inference with complicated models, and Hamiltonian Monte Carlo, in particular Riemannian Manifold Hamiltonian Monte Carlo (RMHMC), has demonstrated impressive success in many…

Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond Statistics. A full exposition of Markov chains and their use…

In this article, we analyze Hamiltonian Monte Carlo (HMC) by placing it in the setting of Riemannian geometry using the Jacobi metric, so that each step corresponds to a geodesic on a suitable Riemannian manifold. We then combine the notion…

We give the first rigorous proof of the convergence of Riemannian Hamiltonian Monte Carlo, a general (and practical) method for sampling Gibbs distributions. Our analysis shows that the rate of convergence is bounded in terms of natural…

Riemannian manifold Hamiltonian (RMHMC) and Lagrangian Monte Carlo (LMC) have emerged as powerful methods of Bayesian inference. Unlike Euclidean Hamiltonian Monte Carlo (EHMC) and the Metropolis-adjusted Langevin algorithm (MALA), the…

With its systematic exploration of probability distributions, Hamiltonian Monte Carlo is a potent Markov Chain Monte Carlo technique; it is an approach, however, ultimately contingent on the choice of a suitable Hamiltonian function. By…

Contributed discussion and rejoinder to "Geodesic Monte Carlo on Embedded Manifolds" (arXiv:1301.6064)

Markov Chain Monte Carlo methods have revolutionised mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of…

In this paper we address the widely-experienced difficulty in tuning Hamiltonian-based Monte Carlo samplers. We develop an algorithm that allows for the adaptation of Hamiltonian and Riemann manifold Hamiltonian Monte Carlo samplers using…

Sampling from hierarchical Bayesian models is often difficult for MCMC methods, because of the strong correlations between the model parameters and the hyperparameters. Recent Riemannian manifold Hamiltonian Monte Carlo (RMHMC) methods have…

We merge in this note our two discussions about the Read Paper "Particle Markov chain Monte Carlo" (Andrieu, Doucet, and Holenstein, 2010) presented on October 16th 2009 at the Royal Statistical Society, appearing in the Journal of the…

The randomized midpoint Langevin Monte Carlo (RLMC), introduced by Shen and Lee (2019), is a variant of classical Unadjusted Langevin Algorithm. It was shown in the literature that the RLMC is an efficient algorithm for approximating…

Monte Carlo techniques have been widely employed in statistical physics as well as in quantum theory in the Lagrangian formulation. However, in some areas of application to quantum theories computational progress has been slow. Here we…

From its inception in the 1950s to the modern frontiers of applied statistics, Markov chain Monte Carlo has been one of the most ubiquitous and successful methods in statistical computing. In that time its development has been fueled by…

This paper provides a convergence analysis for generalized Hamiltonian Monte Carlo samplers, a family of Markov Chain Monte Carlo methods based on leapfrog integration of Hamiltonian dynamics and kinetic Langevin diffusion, that encompasses…

Langevin algorithms are popular Markov chain Monte Carlo methods that are often used to solve high-dimensional large-scale sampling problems in machine learning. The most classical Langevin Monte Carlo algorithm is based on the overdamped…

The Hamiltonian Monte Carlo (HMC) method has been recognized as a powerful sampling tool in computational statistics. We show that performance of HMC can be significantly improved by incorporating importance sampling and an irreversible…