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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…

Likelihood-free methods, such as approximate Bayesian computation, are powerful tools for practical inference problems with intractable likelihood functions. Markov chain Monte Carlo and sequential Monte Carlo variants of approximate…

We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the…

In this paper, we propose an efficient pseudo-marginal Markov chain Monte Carlo (MCMC) sampling approach to draw samples from posterior shape distributions for image segmentation. The computation time of the proposed approach is independent…

The Yule--Simon distribution has been out of the radar of the Bayesian community, so far. In this note, we propose an explicit Gibbs sampling scheme when a Gamma prior is chosen for the shape parameter. The performance of the algorithm is…

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.…

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…

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…

Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…

We deal with Bayesian inference for Beta autoregressive processes. We restrict our attention to the class of conditionally linear processes. These processes are particularly suitable for forecasting purposes, but are difficult to estimate…

Bayesian optimization through Gaussian process regression is an effective method of optimizing an unknown function for which every measurement is expensive. It approximates the objective function and then recommends a new measurement point…

Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…

This paper explores Bayesian inference for a biased sampling model in situations where the population of interest cannot be sampled directly, but rather through an indirect and inherently biased method. Observations are viewed as being the…

Markov chain Monte Carlo (MCMC) provides a feasible method for inferring Hidden Markov models, however, it is often computationally prohibitive, especially constrained by the curse of dimensionality, as the Monte Carlo sampler traverses…

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…

We derive rates of contraction of posterior distributions on nonparametric or semiparametric models based on Gaussian processes. The rate of contraction is shown to depend on the position of the true parameter relative to the reproducing…

While the Matrix Generalized Inverse Gaussian ($\mathcal{MGIG}$) distribution arises naturally in some settings as a distribution over symmetric positive semi-definite matrices, certain key properties of the distribution and effective ways…

Bayesian binary regression is a prosperous area of research due to the computational challenges encountered by currently available methods either for high-dimensional settings or large datasets, or both. In the present work, we focus on the…

Bayesian inference with Markov Chain Monte Carlo (MCMC) is challenging when the likelihood function is irregular and expensive to compute. We explore several sampling algorithms that make use of subset evaluations to reduce computational…

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…