Related papers: An improved implicit sampling for Bayesian inverse…

In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that…

Bayesian low-rank matrix factorization techniques have become an essential tool for relational data analysis and matrix completion. A standard approach is to assign zero-mean Gaussian priors on the columns or rows of factor matrices to…

In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…

It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…

In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior…

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…

This paper concerns the Bayesian approach to inverse acoustic scattering problems of inferring the position and shape of a sound-soft obstacle from phaseless far-field data generated by point source waves. To improve the convergence rate,…

We study Bayesian estimation of mixture models and argue in favor of fitting the marginal posterior distribution over component assignments directly, rather than Gibbs sampling from the joint posterior on components and parameters as is…

We study the Electrical Impedance Tomography Bayesian inverse problem for recovering the conductivity given noisy measurements of the voltage on some boundary surface electrodes. The uncertain conductivity depends linearly on a countable…

Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption,…

We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…

This paper focuses on a challenging class of inverse problems that is often encountered in applications. The forward model is a complex non-linear black-box, potentially non-injective, whose outputs cover multiple decades in amplitude.…

Likelihood-free inference methods based on neural conditional density estimation were shown to drastically reduce the simulation burden in comparison to classical methods such as ABC. When applied in the context of any latent variable…

One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…

We consider the problem of Bayesian inference for bi-variate data observed in time but with observation times which occur non-synchronously. In particular, this occurs in a wide variety of applications in finance, such as high-frequency…

Markov chain Monte Carlo (MCMC) allows one to generate dependent replicates from a posterior distribution for effectively any Bayesian hierarchical model. However, MCMC can produce a significant computational burden. This motivates us to…

Recent studies demonstrate that diffusion models can serve as a strong prior for solving inverse problems. A prominent example is Diffusion Posterior Sampling (DPS), which approximates the posterior distribution of data given the measure…

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…

Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo (MCMC) with simple proposal mechanisms. This hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper,…

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…