Related papers: Posterior Uncertainty Estimation via a Monte Carlo…

Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…

Approximate Bayesian computation (ABC) is computationally intensive for complex model simulators. To exploit expensive simulations, data-resampling via bootstrapping can be employed to obtain many artificial datasets at little cost.…

We provide a clear and concise introduction to the subjects of inverse problems and data assimilation, and their inter-relations. The first part of our notes covers inverse problems; this refers to the study of how to estimate unknown model…

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…

In the context of computer models, calibration is the process of estimating unknown simulator parameters from observational data. Calibration is variously referred to as model fitting, parameter estimation/inference, an inverse problem, and…

Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman…

Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

Monte Carlo (MC) integration is the de facto method for approximating the predictive distribution of Bayesian neural networks (BNNs). But, even with many MC samples, Gaussian-based BNNs could still yield bad predictive performance due to…

Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…

Stochastic parameterizations are increasingly being used to represent the uncertainty associated with model errors in ensemble forecasting and data assimilation. One of the challenges associated with the use of these parameterizations is…

This paper presents a hierarchical Bayesian modeling framework for the uncertainty quantification in modal identification of linear dynamical systems using multiple vibration data sets. This novel framework integrates the state-of-the-art…

Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are…

A Monte Carlo-based Bayesian inference model is applied to the prediction of reactor operation parameters of a PWR nuclear power plant. In this non-perturbative framework, high-dimensional covariance information describing the uncertainty…

Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take…

Even though Bayesian neural networks offer a promising framework for modeling uncertainty, active learning and incorporating prior physical knowledge, few applications of them can be found in the context of interatomic force modeling. One…

Popular approaches for quantifying predictive uncertainty in deep neural networks often involve distributions over weights or multiple models, for instance via Markov Chain sampling, ensembling, or Monte Carlo dropout. These techniques…

Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…

Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…

The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…