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Replication of scientific studies is important for assessing the credibility of their results. However, there is no consensus on how to quantify the extent to which a replication study replicates an original result. We propose a novel…

This paper investigates the consistency of a posterior distribution in the single-measurement fractional Calder\'on problem with additive Gaussian noise. We consider a Bayesian framework with rescaled and Gaussian sieve priors, using a…

Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…

This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…

We study the problem of sampling from the power posterior distribution in Bayesian Gaussian mixture models, a robust version of the classical posterior. This power posterior is known to be non-log-concave and multi-modal, which leads to…

The Laplace approximation is an old, but frequently used method to approximate integrals for Bayesian calculations. In this paper we develop an extension of the Laplace approximation, by applying it iteratively to the residual, i.e., the…

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…

We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious…

Solving inverse problems using Bayesian methods can become prohibitively expensive when likelihood evaluations involve complex and large scale numerical models. A common approach to circumvent this issue is to approximate the forward model…

In this paper, we propose a progressive Bayesian procedure, where the measurement information is continuously included into the given prior estimate (although we perform observations at discrete time steps). The key idea is to derive a…

Density estimation represents one of the most successful applications of Bayesian nonparametrics. In particular, Dirichlet process mixtures of normals are the gold standard for density estimation and their asymptotic properties have been…

We consider inverse problems in Hilbert spaces under correlated Gaussian noise and use a Bayesian approach to find their regularised solution. We focus on mildly ill-posed inverse problems with the noise being generalised derivative of…

We develop an iterative framework for Bayesian inference problems where the posterior distribution may involve computationally intensive models, intractable gradients, significant posterior concentration, and pronounced non-Gaussianity. Our…

We consider the statistical linear inverse problem of making inference on an unknown source function in an elliptic partial differential equation from noisy observations of its solution. We employ nonparametric Bayesian procedures based on…

We introduce the concept of conjugate prior models for a given likelihood function in Bayesian spatial inversion. The conjugate class of prior models can be selection extended and still remain conjugate. We demonstrate the generality of…

The current standard Bayesian approach to model calibration, which assigns a Gaussian process prior to the discrepancy term, often suffers from issues of unidentifiability and computational complexity and instability. When the goal is to…

Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented,…

This paper considers a Bayesian approach for inclusion detection in nonlinear inverse problems using two known and popular push-forward prior distributions: the star-shaped and level set prior distributions. We analyze the convergence of…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

We present a novel Bayesian framework for inverse problems in which the pos terior distribution is interpreted as the intensity measure of a Poisson point process (PPP). The posterior density is approximated using kernel density estimation,…