English
Related papers

Related papers: A Gibbs sampler on the $n$-simplex

200 papers

We study the problem of sampling from the power posterior distribution in Bayesian Gaussian mixture models, a robust version of the classical posterior. This power posterior is known to be non-log-concave and multi-modal, which leads to…

Machine Learning · Statistics 2019-12-12 Wenlong Mou , Nhat Ho , Martin J. Wainwright , Peter L. Bartlett , Michael I. Jordan

We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the…

Statistics Theory · Mathematics 2010-02-26 Minjung Kyung , Jeff Gill , George Casella

In this paper we address the questions of perfectly sampling a Gibbs measure with infinite range interactions and of perfectly sampling the measure together with its finite range approximations. We solve these questions by introducing a…

Probability · Mathematics 2015-05-13 Antonio Galves , Eva Loecherbach , Enza Orlandi

The maximum independent set (MIS) problem is a well-studied combinatorial optimization problem that naturally arises in many applications, such as wireless communication, information theory and statistical mechanics. MIS problem is NP-hard,…

Discrete Mathematics · Computer Science 2015-04-20 Rémi Varloot , Ana Bušić , Anne Bouillard

The pairwise influence matrix of Dobrushin has long been used as an analytical tool to bound the rate of convergence of Gibbs sampling. In this work, we use Dobrushin influence as the basis of a practical tool to certify and efficiently…

Machine Learning · Statistics 2017-07-20 Ioannis Mitliagkas , Lester Mackey

Gibbs sampling is a widely used Markov chain Monte Carlo (MCMC) method for numerically approximating integrals of interest in Bayesian statistics and other mathematical sciences. Many implementations of MCMC methods do not extend easily to…

Computation · Statistics 2019-06-03 Alexander Terenin , Shawfeng Dong , David Draper

We characterise the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence…

Methodology · Statistics 2007-10-24 Omiros Papaspiliopoulos , Gareth Roberts

This paper proposes and compares two new sampling schemes for sparse deconvolution using a Bernoulli-Gaussian model. To tackle such a deconvolution problem in a blind and unsupervised context, the Markov Chain Monte Carlo (MCMC) framework…

Numerical Analysis · Computer Science 2009-09-18 D. Ge , J. Idier , E. Le Carpentier

We present a Dirichlet process mixture model over discrete incomplete rankings and study two Gibbs sampling inference techniques for estimating posterior clusterings. The first approach uses a slice sampling subcomponent for estimating…

Machine Learning · Computer Science 2012-03-19 Marina Meila , Harr Chen

In any Markov chain Monte Carlo analysis, rapid convergence of the chain to its target probability distribution is of practical and theoretical importance. A chain that converges at a geometric rate is geometrically ergodic. In this paper,…

Computation · Statistics 2012-10-05 Alicia A. Johnson , Owen Burbank

Sampling from the lattice Gaussian distribution has emerged as an important problem in coding, decoding and cryptography. In this paper, lattice reduction technique is adopted to Gibbs sampler for lattice Gaussian sampling. Firstly, with…

Information Theory · Computer Science 2018-12-04 Zheng Wang , Yang Huang , Shanxiang Lyu

We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…

Computation · Statistics 2019-06-27 Giacomo Zanella , Gareth Roberts

We consider Markov chain Monte Carlo (MCMC) algorithms for Bayesian high-dimensional regression with continuous shrinkage priors. A common challenge with these algorithms is the choice of the number of iterations to perform. This is…

Methodology · Statistics 2021-07-13 Niloy Biswas , Anirban Bhattacharya , Pierre E. Jacob , James E. Johndrow

This paper considers how to obtain MCMC quantitative convergence bounds which can be translated into tight complexity bounds in high-dimensional {settings}. We propose a modified drift-and-minorization approach, which establishes…

Computation · Statistics 2022-05-12 Jun Yang , Jeffrey S. Rosenthal

We present a new notion of probabilistic duality for random variables involving mixture distributions. Using this notion, we show how to implement a highly-parallelizable Gibbs sampler for weakly coupled discrete pairwise graphical models…

Machine Learning · Computer Science 2016-11-23 Lars Mescheder , Sebastian Nowozin , Andreas Geiger

Markov Chain Monte Carlo (MCMC) methods such as Gibbs sampling are finding widespread use in applied statistics and machine learning. These often lead to difficult computational problems, which are increasingly being solved on parallel and…

Machine Learning · Statistics 2018-06-05 Alexander Terenin , Eric P. Xing

This paper outlines a Bayesian approach to estimate finite mixtures of Tobit models. The method consists of an MCMC approach that combines Gibbs sampling with data augmentation and is simple to implement. I show through simulations that the…

Econometrics · Economics 2024-11-18 Caio Waisman

Asynchronous Gibbs sampling has been recently shown to be fast-mixing and an accurate method for estimating probabilities of events on a small number of variables of a graphical model satisfying Dobrushin's condition~\cite{DeSaOR16}. We…

Machine Learning · Computer Science 2018-11-27 Constantinos Daskalakis , Nishanth Dikkala , Siddhartha Jayanti

Markov jump processes (MJPs) are continuous-time stochastic processes widely used in a variety of applied disciplines. Inference for MJPs typically proceeds via Markov chain Monte Carlo, the state-of-the-art being a uniformization-based…

Computation · Statistics 2020-04-14 Boqian Zhang , Vinayak Rao

The K-Mean and EM algorithms are popular in clustering and mixture modeling, due to their simplicity and ease of implementation. However, they have several significant limitations. Both coverage to a local optimum of their respective…

Machine Learning · Computer Science 2013-01-18 Ian Davidson