Related papers: Covariant priors and model uncertainty

In this dissertation, an abstract formalism extending information geometry is introduced. This framework encompasses a broad range of modelling problems, including possible applications in machine learning and in the information theoretical…

Covariance matrix estimation arises in multivariate problems including multivariate normal sampling models and regression models where random effects are jointly modeled, e.g. random-intercept, random-slope models. A Bayesian analysis of…

We consider joint inversion for two or more unknown parameters from observational data in the Bayesian framework. Standard approaches often either treat the parameters as independent or impose structural similarity through regularisation…

The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…

Complex models in physics, biology, economics, and engineering are often sloppy, meaning that the model parameters are not well determined by the model predictions for collective behavior. Many parameter combinations can vary over decades…

Equivariant models leverage prior knowledge on symmetries to improve predictive performance, but misspecified architectural constraints can harm it instead. While work has explored learning or relaxing constraints, selecting among…

In this work, we investigate the use of Besov priors in the context of Bayesian inverse problems. The solution to Bayesian inverse problems is the posterior distribution which naturally enables us to interpret the uncertainties. Besov…

The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…

We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the…

The interplay between missing data and model uncertainty -- two classic statistical problems -- leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the…

Variational Bayesian posterior inference often requires simplifying approximations such as mean-field parametrisation to ensure tractability. However, prior work has associated the variational mean-field approximation for Bayesian neural…

Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information,…

Variance parameter estimation in linear mixed models is a challenge for many classical nonlinear optimization algorithms due to the positive-definiteness constraint of the random effects covariance matrix. We take a completely novel view on…

Forecasting techniques for assessing the power of future experiments to discriminate between theories or discover new laws of nature are of great interest in many areas of science. In this paper, we introduce a Bayesian forecasting method…

We introduce a prior for the parameters of univariate continuous distributions, based on the Wasserstein information matrix, which is invariant under reparameterisations. We discuss the links between the proposed prior with information…

A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…

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…

Bayesian inference paradigms are regarded as powerful tools for solution of inverse problems. However, when applied to inverse problems in physical sciences, Bayesian formulations suffer from a number of inconsistencies that are often…