Related papers: Scalable Rejection Sampling for Bayesian Hierarchi…
Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…
Markov Chain Monte Carlo (MCMC) methods are a popular technique in Bayesian statistical modeling. They have long been used to obtain samples from posterior distributions, but recent research has focused on the scalability of these…
We present a sequential Monte Carlo sampler algorithm for the Bayesian analysis of generalised linear mixed models (GLMMs). These models support a variety of interesting regression-type analyses, but performing inference is often extremely…
Advances in digital sensors, digital data storage and communications have resulted in systems being capable of accumulating large collections of data. In the light of dealing with the challenges that massive data present, this work proposes…
This work introduces a new method designed for Bayesian deep learning called scalable Bayesian Monte Carlo (SBMC). The method is comprised of a model and an algorithm. The model interpolates between a point estimator and the posterior. The…
This paper deals with some computational aspects in the Bayesian analysis of statistical models with intractable normalizing constants. In the presence of intractable normalizing constants in the likelihood function, traditional MCMC…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior…
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…
Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…
A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution. Markov Chain Monte Carlo is a fundamental tool to consistently compute these expectations via averaging samples drawn…
We propose a sequential Markov chain Monte Carlo (SMCMC) algorithm to sample from a sequence of probability distributions, corresponding to posterior distributions at different times in on-line applications. SMCMC proceeds as in usual MCMC…
Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…
We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent…
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,…
We propose a very fast approximate Markov Chain Monte Carlo (MCMC) sampling framework that is applicable to a large class of sparse Bayesian inference problems, where the computational cost per iteration in several models is of order…
Markov chain Monte Carlo (MCMC) methods asymptotically sample from complex probability distributions. The pseudo-marginal MCMC framework only requires an unbiased estimator of the unnormalized probability distribution function to construct…
There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…
In many hierarchical inverse problems, not only do we want to estimate high- or infinite-dimensional model parameters in the parameter-to-observable maps, but we also have to estimate hyperparameters that represent critical assumptions in…