Related papers: Bayesian Solution Uncertainty Quantification for D…
We provide a general solution to a fundamental open problem in Bayesian inference, namely poor uncertainty quantification, from a frequency standpoint, of Bayesian methods in misspecified models. While existing solutions are based on…
We develop a new Bayesian model for non-rigid registration of three-dimensional medical images, with a focus on uncertainty quantification. Probabilistic registration of large images with calibrated uncertainty estimates is difficult for…
Predicting outcomes in external domains is challenging due to hidden confounders that potentially influence both predictors and outcomes. Well-established methods frequently rely on stringent assumptions, explicit knowledge about the…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
Calibration or parameter identification is used with computational mechanics models related to observed data of the modeled process to find model parameters such that good similarity between model prediction and observation is achieved. We…
Probabilistic (or Bayesian) modeling and learning offers interesting possibilities for systematic representation of uncertainty using probability theory. However, probabilistic learning often leads to computationally challenging problems.…
We introduce a novel uncertainty estimation for classification tasks for Bayesian convolutional neural networks with variational inference. By normalizing the output of a Softplus function in the final layer, we estimate aleatoric and…
Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
How might a smooth probability distribution be estimated, with accurately quantified uncertainty, from a limited amount of sampled data? Here we describe a field-theoretic approach that addresses this problem remarkably well in one…
Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…
Statistical models typically capture uncertainties in our knowledge of the corresponding real-world processes, however, it is less common for this uncertainty specification to capture uncertainty surrounding the values of the inputs to the…
In many problems of data-driven modeling for dynamical systems, the governing equations are not known a priori and must be selected phenomenologically from a large set of candidate interactions and basis functions. In such situations, point…
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…
Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…
A new Bayesian approach to linear system identification has been proposed in a series of recent papers. The main idea is to frame linear system identification as predictor estimation in an infinite dimensional space, with the aid of…
This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…
A common problem in data analysis is that the functional form, as well as the parameter values, of the underlying model which should describe a dataset is not known a priori. In these cases some extra uncertainty must be assigned to the…
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…