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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…

Data Analysis, Statistics and Probability · Physics 2013-05-29 Fergal P. Casey , Joshua J. Waterfall , Ryan N. Gutenkunst , Christopher R. Myers , James P. Sethna

In engineering examples, one often encounters the need to sample from unnormalized distributions with complex shapes that may also be implicitly defined through a physical or numerical simulation model, making it computationally expensive…

Methodology · Statistics 2024-11-27 Promit Chakroborty , Michael D. Shields

The particle Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm to sample from the full posterior distribution of a state-space model. It does so by executing Gibbs sampling steps on an extended target distribution defined on the…

Computation · Statistics 2015-07-29 Nicolas Chopin , Sumeetpal S. Singh

Markov chain Monte Carlo (MCMC) algorithms are based on the construction of a Markov chain with transition probabilities leaving invariant a probability distribution of interest. In this work, we look at these transition probabilities as…

Probability · Mathematics 2024-10-01 Rocco Caprio , Adam M. Johansen

Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal…

Machine Learning · Computer Science 2018-11-13 Rohitash Chandra , Konark Jain , Ratneel V. Deo , Sally Cripps

We propose Adaptive Incremental Mixture Markov chain Monte Carlo (AIMM), a novel approach to sample from challenging probability distributions defined on a general state-space. While adaptive MCMC methods usually update a parametric…

Methodology · Statistics 2018-06-01 Florian Maire , Nial Friel , Antonietta Mira , Adrian Raftery

We propose a novel approximate inference algorithm that approximates a target distribution by amortising the dynamics of a user-selected MCMC sampler. The idea is to initialise MCMC using samples from an approximation network, apply the…

Machine Learning · Statistics 2017-05-23 Yingzhen Li , Richard E. Turner , Qiang Liu

Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…

Computational Physics · Physics 2026-02-16 Michael Kim , Wei Cai

Effective implementations of sampling-based probabilistic inference often require manually constructed, model-specific proposals. Inspired by recent progresses in meta-learning for training learning agents that can generalize to unseen…

Artificial Intelligence · Computer Science 2019-01-03 Tongzhou Wang , Yi Wu , David A. Moore , Stuart J. Russell

Markov Chain Monte Carlo methods are widely used in signal processing and communications for statistical inference and stochastic optimization. In this work, we introduce an efficient adaptive Metropolis-Hastings algorithm to draw samples…

Computation · Statistics 2016-03-17 David Luengo , Luca Martino

Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a…

High Energy Physics - Phenomenology · Physics 2023-09-06 N. T. Hunt-Smith , W. Melnitchouk , F. Ringer , N. Sato , A. W Thomas , M. J. White

Markov chain Monte Carlo algorithms are used to simulate from complex statistical distributions by way of a local exploration of these distributions. This local feature avoids heavy requests on understanding the nature of the target, but it…

Computation · Statistics 2018-04-12 Christian P. Robert , Victor Elvira , Nick Tawn , Changye Wu

Segmenting images of low quality or with missing data is a challenging problem. Integrating statistical prior information about the shapes to be segmented can improve the segmentation results significantly. Most shape-based segmentation…

Computer Vision and Pattern Recognition · Computer Science 2016-11-14 Ertunc Erdil , Sinan Yıldırım , Müjdat Çetin , Tolga Taşdizen

Markov Chain Monte Carlo (MCMC) methods are algorithms for sampling probability distributions, commonly applied to the Boltzmann distribution in physical and chemical models such as protein folding and the Ising model. These methods enable…

Quantum Physics · Physics 2025-12-04 Aingeru Ramos , Jose A. Pascual , Javier Navaridas , Ivan Coluzza

Markov Chain Monte Carlo (MCMC) methods have a drawback when working with a target distribution or likelihood function that is computationally expensive to evaluate, specially when working with big data. This paper focuses on…

Machine Learning · Computer Science 2019-10-22 Asif J. Chowdhury , Gabriel Terejanu

A simple and efficient adaptive Markov Chain Monte Carlo (MCMC) method, called the Metropolized Adaptive Subspace (MAdaSub) algorithm, is proposed for sampling from high-dimensional posterior model distributions in Bayesian variable…

Methodology · Statistics 2023-01-04 Christian Staerk , Maria Kateri , Ioannis Ntzoufras

In this work, we introduce a novel class of adaptive Monte Carlo methods, called adaptive independent sticky MCMC algorithms, for efficient sampling from a generic target probability density function (pdf). The new class of algorithms…

Computation · Statistics 2025-04-09 L. Martino , R. Casarin , F. Leisen , D. Luengo

Improving efficiency of importance sampler is at the center of research in Monte Carlo methods. While adaptive approach is usually difficult within the Markov Chain Monte Carlo framework, the counterpart in importance sampling can be…

Methodology · Statistics 2007-12-11 Heng Lian

Training energy-based probabilistic models is confronted with apparently intractable sums, whose Monte Carlo estimation requires sampling from the estimated probability distribution in the inner loop of training. This can be approximately…

Machine Learning · Computer Science 2016-06-13 Taesup Kim , Yoshua Bengio

We propose a method to construct a proposal density for the Metropolis-Hastings algorithm in Markov Chain Monte Carlo (MCMC) simulations of the GARCH model. The proposal density is constructed adaptively by using the data sampled by the…

Computational Finance · Quantitative Finance 2009-07-14 Tetsuya Takaishi