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In Bayesian inference, predictive distributions are typically in the form of samples generated via Markov chain Monte Carlo (MCMC) or related algorithms. In this paper, we conduct a systematic analysis of how to make and evaluate…
We introduce a new Markov-Chain Monte Carlo (MCMC) approach designed for efficient sampling of highly correlated and multimodal posteriors. Parallel tempering, though effective, is a costly technique for sampling such posteriors. Our…
Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from…
Monte Carlo (MC) integration is the de facto method for approximating the predictive distribution of Bayesian neural networks (BNNs). But, even with many MC samples, Gaussian-based BNNs could still yield bad predictive performance due to…
In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic…
Integration over non-negative integrands is a central problem in machine learning (e.g. for model averaging, (hyper-)parameter marginalisation, and computing posterior predictive distributions). Bayesian Quadrature is a probabilistic…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
We show how to speed up Sequential Monte Carlo (SMC) for Bayesian inference in large data problems by data subsampling. SMC sequentially updates a cloud of particles through a sequence of distributions, beginning with a distribution that is…
The Metropolis-Hastings (MH) algorithm is one of the most widely used Markov Chain Monte Carlo schemes for generating samples from Bayesian posterior distributions. The algorithm is asymptotically exact, flexible and easy to implement.…
The Hamiltonian Monte Carlo (HMC) method allows sampling from continuous densities. Favorable scaling with dimension has led to wide adoption of HMC by the statistics community. Modern auto-differentiating software should allow more…
In this article, we describe a {\tt R} package for sampling from an empirical likelihood-based posterior using a Hamiltonian Monte Carlo method. Empirical likelihood-based methodologies have been used in Bayesian modeling of many problems…
We study probit regression from a Bayesian perspective and give an alternative form for the posterior distribution when the prior distribution for the regression parameters is the uniform distribution. This new form allows simple Monte…
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…
Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to…
In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by…
Markov Chain Monte Carlo inference of target posterior distributions in machine learning is predominately conducted via Hamiltonian Monte Carlo and its variants. This is due to Hamiltonian Monte Carlo based samplers ability to suppress…
While Bayesian methods are extremely popular in statistics and machine learning, their application to massive datasets is often challenging, when possible at all. Indeed, the classical MCMC algorithms are prohibitively slow when both the…
The Linear Ballistic Accumulator (Brown & Heathcote, 2008) model is used as a measurement tool to answer questions about applied psychology. The analyses based on this model depend upon the model selected and its estimated parameters.…