Related papers: An adaptive approximate Bayesian computation MCMC …

The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…

Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC.…

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their scalability…

Bayesian inference in the presence of an intractable likelihood function is computationally challenging. When following a Markov chain Monte Carlo (MCMC) approach to approximate the posterior distribution in this context, one typically…

Bayesian inference provides a methodology for parameter estimation and uncertainty quantification in machine learning and deep learning methods. Variational inference and Markov Chain Monte-Carlo (MCMC) sampling methods are used to…

Approximate Bayesian computation methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper we discuss and apply an approximate Bayesian computation (ABC) method based on sequential Monte…

Approximate Bayesian computation (ABC) refers to a family of inference methods used in the Bayesian analysis of complex models where evaluation of the likelihood is difficult. Conventional ABC methods often suffer from the curse of…

Recently, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have been proposed for scaling up Monte Carlo computations to large data problems. Whilst these approaches have proven useful in many applications, vanilla SG-MCMC…

We introduce Markov chain Monte Carlo (MCMC) algorithms based on numerical approximations of piecewise-deterministic Markov processes obtained with the framework of splitting schemes. We present unadjusted as well as adjusted algorithms,…

Performing reliable Bayesian inference on a big data scale is becoming a keystone in the modern era of machine learning. A workhorse class of methods to achieve this task are Markov chain Monte Carlo (MCMC) algorithms and their design to…

Composite likelihood provides approximate inference when the full likelihood is intractable and sub-likelihood functions of marginal events can be evaluated relatively easily. It has been successfully applied for many complex models.…

This book aims to provide a graduate-level introduction to advanced topics in Markov chain Monte Carlo (MCMC) algorithms, as applied broadly in the Bayesian computational context. Most, if not all of these topics (stochastic gradient MCMC,…

Multidimensional scaling (MDS) is widely used to reconstruct a low-dimensional representation of high-dimensional data while preserving pairwise distances. However, Bayesian MDS approaches based on Markov chain Monte Carlo (MCMC) face…

We study Bayesian inversion for a model elliptic PDE with unknown diffusion coefficient. We provide complexity analyses of several Markov Chain-Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the…

Markov Chain Monte Carlo (MCMC) methods are a powerful tool for computation with complex probability distributions. However the performance of such methods is critically dependant on properly tuned parameters, most of which are difficult if…

Approximate Bayesian Computational (ABC) methods (or likelihood-free methods) have appeared in the past fifteen years as useful methods to perform Bayesian analyses when the likelihood is analytically or computationally intractable. Several…

Tasks such as record linkage and multi-target tracking, which involve reconstructing the set of objects that underlie some observed data, are particularly challenging for probabilistic inference. Recent work has achieved efficient and…

Sequential algorithms such as sequential importance sampling (SIS) and sequential Monte Carlo (SMC) have proven fundamental in Bayesian inference for models not admitting a readily available likelihood function. For approximate Bayesian…

Markov chain Monte Carlo (MCMC) algorithms are widely used to sample from complicated distributions, especially to sample from the posterior distribution in Bayesian inference. However, MCMC is not directly applicable when facing the doubly…

We propose new Markov Chain Monte Carlo algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of set-valued maps in the proposal step of the MCMC algorithms. The motivation for…