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Related papers: MCMC for Normalized Random Measure Mixture Models

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Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud…

Sequential Monte Carlo (SMC) is a methodology for sampling approximately from a sequence of probability distributions of increasing dimension and estimating their normalizing constants. We propose here an alternative methodology named…

Statistics Theory · Mathematics 2012-11-13 Anthony Brockwell , Pierre Del Moral , Arnaud Doucet

Recent advances in machine learning have led to the development of new methods for enhancing Monte Carlo methods such as Markov chain Monte Carlo (MCMC) and importance sampling (IS). One such method is normalizing flows, which use a neural…

Computation · Statistics 2024-01-12 Charly Andral

Practitioners of Bayesian statistics have long depended on Markov chain Monte Carlo (MCMC) to obtain samples from intractable posterior distributions. Unfortunately, MCMC algorithms are typically serial, and do not scale to the large…

Machine Learning · Statistics 2015-06-11 Maxim Rabinovich , Elaine Angelino , Michael I. Jordan

Bayesian low-rank matrix factorization techniques have become an essential tool for relational data analysis and matrix completion. A standard approach is to assign zero-mean Gaussian priors on the columns or rows of factor matrices to…

Machine Learning · Statistics 2020-11-11 Saibal De , Hadi Salehi , Alex Gorodetsky

The Markov Chain Monte Carlo (MCMC) algorithm is a widely recognised as an efficient method for sampling a specified posterior distribution. However, when the posterior is multi-modal, conventional MCMC algorithms either tend to become…

Instrumentation and Methods for Astrophysics · Physics 2014-08-19 Yi-Ming Hu , Martin Hendry , Ik Siong Heng

Markov chain Monte Carlo (MCMC) is the engine of modern Bayesian statistics, being used to approximate the posterior and derived quantities of interest. Despite this, the issue of how the output from a Markov chain is post-processed and…

Methodology · Statistics 2021-09-07 Leah F. South , Marina Riabiz , Onur Teymur , Chris. J. Oates

Posterior sampling is a task of central importance in Bayesian inference. For many applications in Bayesian meta-analysis and Bayesian transfer learning, the prior distribution is unknown and needs to be estimated from samples. In practice,…

Computation · Statistics 2024-08-06 Chenyang Zhong , Shouxuan Ji , Tian Zheng

Monte Carlo methods -- such as Markov chain Monte Carlo (MCMC) and piecewise deterministic Markov process (PDMP) samplers -- provide asymptotically exact estimators of expectations under a target distribution. There is growing interest in…

Computation · Statistics 2024-09-09 Adrien Corenflos , Matthew Sutton , Nicolas Chopin

Markov chain Monte Carlo (MCMC) is a simulation method commonly used for estimating expectations with respect to a given distribution. We consider estimating the covariance matrix of the asymptotic multivariate normal distribution of a…

Methodology · Statistics 2017-06-06 Ning Dai , Galin L. Jones

The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…

Machine Learning · Statistics 2014-04-08 Maurizio Filippone , Mark Girolami

We investigate the efficiency of a marginal likelihood estimator where the product of the marginal posterior distributions is used as an importance-sampling function. The approach is generally applicable to multi-block parameter vector…

Computation · Statistics 2014-07-08 K. Perrakis , I. Ntzoufras , E. G. Tsionas

Due to the escalating growth of big data sets in recent years, new Bayesian Markov chain Monte Carlo (MCMC) parallel computing methods have been developed. These methods partition large data sets by observations into subsets. However, for…

Methodology · Statistics 2019-01-21 Zheng Wei , Erin M. Conlon

This paper presents a new Markov chain Monte Carlo method to sample from the posterior distribution of conjugate mixture models. This algorithm relies on a flexible split-merge procedure built using the particle Gibbs sampler. Contrary to…

Computation · Statistics 2017-05-30 Alexandre Bouchard-Côté , Arnaud Doucet , Andrew Roth

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…

Computation · Statistics 2019-12-10 Dootika Vats , Nathan Robertson , James M Flegal , Galin L Jones

Markov chain Monte Carlo (MCMC) is widely used for Bayesian inference in models of complex systems. Performance, however, is often unsatisfactory in models with many latent variables due to so-called poor mixing, necessitating development…

Methodology · Statistics 2019-10-25 C. M. Pooley , S. C. Bishop , A. Doeschl-Wilson , G. Marion

Specifying a full Bayesian model that integrates multiple data sources can be challenging. One natural approach is to specify each individual model separately and join them afterwards. This is the approach adopted in Markov melding.…

Methodology · Statistics 2026-05-22 Yixuan Liu , Robert J. B. Goudie

Markov chain Monte Carlo (MCMC) provides a feasible method for inferring Hidden Markov models, however, it is often computationally prohibitive, especially constrained by the curse of dimensionality, as the Monte Carlo sampler traverses…

Artificial Intelligence · Computer Science 2023-09-13 Xiongming Dai , Gerald Baumgartner

We consider the theoretical analysis of Multiscale Sampling Methods, which are a new class of gradient-free Markov chain Monte Carlo (MCMC) methods for high dimensional inverse differential equation problems. A detailed presentation of…

Methodology · Statistics 2025-03-06 Lucas Seiffert , Felipe Pereira

Markov chain Monte Calro methods (MCMC) are commonly used in Bayesian statistics. In the last twenty years, many results have been established for the calculation of the exact convergence rate of MCMC methods. We introduce another rate of…

Statistics Theory · Mathematics 2014-02-17 Kengo Kamatani