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Constitutive model discovery refers to the task of identifying an appropriate model structure, usually from a predefined model library, while simultaneously inferring its material parameters. The data used for model discovery are measured…

Bayesian analyses combine information represented by different terms in a joint Bayesian model. When one or more of the terms is misspecified, it can be helpful to restrict the use of information from suspect model components to modify…

Latent diffusion has demonstrated promising results in image generation and permits efficient sampling. However, this framework might suffer from the problem of posterior collapse when applied to time series. In this paper, we first show…

Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…

This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…

A variational Bayesian inference for measured wave intensity, such as X-ray intensity, is proposed in this paper. The data is popular to obtain information about unobservable features of an object, such as a material sample and the…

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

Variational Bayes (VB) has been used to facilitate the calculation of the posterior distribution in the context of Bayesian inference of the parameters of nonlinear models from data. Previously an analytical formulation of VB has been…

Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense…

We present extensive empirical evidence showing that current Bayesian simulation-based inference algorithms can produce computationally unfaithful posterior approximations. Our results show that all benchmarked algorithms -- (Sequential)…

Gaussian processes (GPs) provide a framework for Bayesian inference that can offer principled uncertainty estimates for a large range of problems. For example, if we consider regression problems with Gaussian likelihoods, a GP model enjoys…

We investigate the convergence rates of variational posterior distributions for statistical inverse problems involving nonlinear partial differential equations (PDEs). Departing from exact Bayesian inference, variational inference…

Mean-field Variational Bayes (MFVB) is an approximate Bayesian posterior inference technique that is increasingly popular due to its fast runtimes on large-scale datasets. However, even when MFVB provides accurate posterior means for…

Bayesian inference is used to estimate continuous parameter values given measured data in many fields of science. The method relies on conditional probability densities to describe information about both data and parameters, yet the notion…

Mean-field variational inference is a method for approximate Bayesian posterior inference. It approximates a full posterior distribution with a factorized set of distributions by maximizing a lower bound on the marginal likelihood. This…

Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (the inverse problem) and prediction (the forward problem)…

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 study addresses an image-matching problem in challenging cases, such as large scene variations or textureless scenes. To gain robustness to such situations, most previous studies have attempted to encode the global contexts of a scene…

Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper…