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Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…

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…

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…

This position paper summarizes a recently developed research program focused on inference in the context of data centric science and engineering applications, and forecasts its trajectory forward over the next decade. Often one endeavours…

Employing Bayesian inference to calibrate constitutive model parameters has grown substantially in recent years. Among the available techniques, Markov Chain Monte Carlo (MCMC) sampling remains one of the most widely used approaches for…

We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. Under such an assumption,…

Computing the marginal likelihood or evidence is one of the core challenges in Bayesian analysis. While there are many established methods for estimating this quantity, they predominantly rely on using a large number of posterior samples…

A Monte Carlo algorithm is said to be adaptive if it automatically calibrates its current proposal distribution using past simulations. The choice of the parametric family that defines the set of proposal distributions is critical for good…

Parallel Markov Chain Monte Carlo (pMCMC) algorithms generate clouds of proposals at each step to efficiently resolve a target probability distribution. We build a rigorous foundational framework for pMCMC algorithms that situates these…

In this article we consider Bayesian parameter inference associated to partially-observed stochastic processes that start from a set B0 and are stopped or killed at the first hitting time of a known set A. Such processes occur naturally…

Markov chain Monte Carlo (MCMC) methods are ubiquitous tools for simulation-based inference in many fields but designing and identifying good MCMC samplers is still an open question. This paper introduces a novel MCMC algorithm, namely,…

Bayesian inference under a set of priors, called robust Bayesian analysis, allows for estimation of parameters within a model and quantification of epistemic uncertainty in quantities of interest by bounded (or imprecise) probability.…

Communication costs, resulting from synchronization requirements during learning, can greatly slow down many parallel machine learning algorithms. In this paper, we present a parallel Markov chain Monte Carlo (MCMC) algorithm in which…

Varying coefficient models (VCMs) are widely used for estimating nonlinear regression functions for functional data. Their Bayesian variants using Gaussian process priors on the functional coefficients, however, have received limited…

Approximate Bayesian computation (ABC) is now an established technique for statistical inference used in cases where the likelihood function is computationally expensive or not available. It relies on the use of a~model that is specified in…

In this article we consider Bayesian estimation of static parameters for a class of partially observed McKean-Vlasov diffusion processes with discrete-time observations over a fixed time interval. This problem features several obstacles to…

We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to…

Markov chain Monte Carlo (MCMC) methods are powerful computational tools for analysis of complex statistical problems. However, their computational efficiency is highly dependent on the chosen proposal distribution, which is generally…

We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for $n$ observations is estimated from a random subset of $m$ observations. We introduce a highly efficient unbiased estimator of the…

In this article we consider computing expectations w.r.t.~probability laws associated to a certain class of stochastic systems. In order to achieve such a task, one must not only resort to numerical approximation of the expectation, but…