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Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…

The log Gaussian Cox process is a flexible class of Cox processes, whose intensity surface is stochastic, for incorporating complex spatial and time structure of point patterns. The straightforward inference based on Markov chain Monte…

We consider Bayesian variable selection for binary outcomes under a probit link with a spike-and-slab prior on the regression coefficients. Motivated by the computational challenges encountered by Markov chain Monte Carlo (MCMC) samplers in…

This paper studies a new and highly efficient Markov chain Monte Carlo (MCMC) methodology to perform Bayesian inference in low-photon imaging problems, with particular attention to situations involving observation noise processes that…

Bayesian estimation strategies represent the most fundamental formulation of the state estimation problem available, and apply readily to nonlinear systems with non-Gaussian uncertainties. The present paper introduces a novel method for…

A novel approach of accurately reconstructing storage ring's linear optics from turn-by-turn (TbT) data containing measurement error is introduced. This approach adopts a Bayesian inference based on the Markov Chain Monte-Carlo (MCMC)…

Deep learning models, such as convolutional neural networks, have long been applied to image and multi-media tasks, particularly those with structured data. More recently, there has been more attention to unstructured data that can be…

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 consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such…

Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking…

The use of non-differentiable priors in Bayesian statistics has become increasingly popular, in particular in Bayesian imaging analysis. Current state of the art methods are approximate in the sense that they replace the posterior with a…

Bayesian statistics is a cornerstone of imaging sciences, underpinning many and varied approaches from Markov random fields to score-based denoising diffusion models. In addition to powerful image estimation methods, the Bayesian paradigm…

In many applications, such as economics, operations research and reinforcement learning, one often needs to estimate a multivariate regression function f subject to a convexity constraint. For example, in sequential decision processes the…

While Robert and Rousseau (2010) addressed the foundational aspects of Bayesian analysis, the current chapter details its practical aspects through a review of the computational methods available for approximating Bayesian procedures.…

We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…

Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed…

We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible,…

Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…

This paper proposes a new methodology to perform Bayesian inference for a class of multidimensional Cox processes in which the intensity function is piecewise constant. Poisson processes with piecewise constant intensity functions are…