相关论文: Continuity of the Solution of a Non-Parametric Bay…

In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations. The models contain uncertain parameters and are indexed by a…

Calibration refers to the estimation of unknown parameters which are present in computer experiments but not available in physical experiments. An accurate estimation of these parameters is important because it provides a scientific…

It is argued that the Calibrated Bayesian (CB) approach to statistical inference capitalizes on the strength of Bayesian and frequentist approaches to statistical inference. In the CB approach, inferences under a particular model are…

These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…

This paper analyzes a popular computational framework to solve infinite-dimensional Bayesian inverse problems, discretizing the prior and the forward model in a finite-dimensional weighted inner product space. We demonstrate the benefit of…

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

In broad applications, it is routinely of interest to assess whether there is evidence in the data to refute the assumption of conditional independence of $Y$ and $X$ conditionally on $Z$. Such tests are well developed in parametric models…

Mobile robotic applications need precise information about the geometric position of the individual sensors on the platform. This information is given by the extrinsic calibration parameters which define how the sensor is rotated and…

We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…

Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…

We introduce Stochastic Asymptotical Regularization (SAR) methods for the uncertainty quantification of the stable approximate solution of ill-posed linear-operator equations, which are deterministic models for numerous inverse problems in…

Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel…

The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…

The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable…

We present a common framework for Bayesian emulation methodologies for multivariate-output simulators, or computer models, that employ either parametric linear models or nonparametric Gaussian processes. Novel diagnostics suitable for…

In this work, we review the theory involved in the Bayesian calibration of complex computer models, with particular emphasis on their use for applications involving computationally expensive simulations and scarce experimental data. In the…

Matching a nonprobability sample to a probability sample is one strategy both for selecting the nonprobability units and for weighting them. This approach has been employed in the past to select subsamples of persons from a large panel of…

The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…

The mean field variational Bayes (VB) algorithm implemented in Stan is relatively fast and efficient, making it feasible to produce model-estimated official statistics on a rapid timeline. Yet, while consistent point estimates of parameters…

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…