Related papers: Statistical guarantees for Bayesian uncertainty qu…

Uncertainty quantification requires efficient summarization of high- or even infinite-dimensional (i.e., non-parametric) distributions based on, e.g., suitable point estimates (modes) for posterior distributions arising from model-specific…

Covariate measurement error in nonparametric regression is a common problem in nutritional epidemiology and geostatistics, and other fields. Over the last two decades, this problem has received substantial attention in the frequentist…

A Bayesian inference method for problems with small samples and sparse data is presented in this paper. A general type of prior ($\propto 1/\sigma^{q}$) is proposed to formulate the Bayesian posterior for inference problems under small…

An established and growing literature on generalized fiducial inference and related fiducial ideas points to the adoption of fiducial inference as a mainstream perspective among modern statisticians. Like Bayesian posteriors, generalized…

Gaussian Process Regression is a popular nonparametric regression method based on Bayesian principles that provides uncertainty estimates for its predictions. However, these estimates are of a Bayesian nature, whereas for some important…

Empirical Bayes methods are widely used for large-scale inference, yet most classical approaches assume homoscedastic observations and focus primarily on posterior mean estimation. We develop a nonparametric empirical Bayes framework for…

In this work, we investigate the estimation of a parameter $f$ in PDEs using Bayesian procedures, and focus on posterior distributions constructed using Gaussian process priors, and its variational approximation. We establish contraction…

The new field of adaptive data analysis seeks to provide algorithms and provable guarantees for models of machine learning that allow researchers to reuse their data, which normally falls outside of the usual statistical paradigm of static…

Berger et al. (2001) and Ren et al. (2012) derived noninformative priors for Gaussian process models of spatially correlated data using the reference prior approach (Berger, Bernardo, 1991). The priors have good statistical properties and…

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…

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

Consider binary observations whose response probability is an unknown smooth function of a set of covariates. Suppose that a prior on the response probability function is induced by a Gaussian process mapped to the unit interval through a…

The Bayesian approach to solving inverse problems relies on the choice of a prior. This critical ingredient allows the formulation of expert knowledge or physical constraints in a probabilistic fashion and plays an important role for the…

Non-Bayesian social learning theory provides a framework for distributed inference of a group of agents interacting over a social network by sequentially communicating and updating beliefs about the unknown state of the world through…

A nonparanormal graphical model is a semiparametric generalization of a Gaussian graphical model for continuous variables in which it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone…

Power posteriors "robustify" standard Bayesian inference by raising the likelihood to a constant fractional power, effectively downweighting its influence in the calculation of the posterior. Power posteriors have been shown to be more…

We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can…

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…

Statisticians often face the choice between using probability models or a paradigm defined by minimising a loss function. Both approaches are useful and, if the loss can be re-cast into a proper probability model, there are many tools to…

Bayesian tests on the symmetry of the generalized von Mises model for planar directions (Gatto and Jammalamadaka, 2007) are introduced. The generalized von Mises distribution is a flexible model that can be axially symmetric or asymmetric,…