Related papers: Optimal projection of observations in a Bayesian s…

In this letter, we consider two sets of observations defined as subspace signals embedded in noise and we wish to analyze the distance between these two subspaces. The latter entails evaluating the angles between the subspaces, an issue…

In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the…

Bayesian optimal experimental design is a principled framework for conducting experiments that leverages Bayesian inference to quantify how much information one can expect to gain from selecting a certain design. However, accurate Bayesian…

As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…

Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…

We propose a dimension reduction technique for Bayesian inverse problems with nonlinear forward operators, non-Gaussian priors, and non-Gaussian observation noise. The likelihood function is approximated by a ridge function, i.e., a map…

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…

Bayesian optimization (BO) has established itself as a leading strategy for efficiently optimizing expensive-to-evaluate functions. Existing BO methods mostly rely on Gaussian process (GP) surrogate models and are not applicable to…

Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The prior is also introduced for the hyperparameters in fully Bayesian inversions…

A Bayesian approach is presented for detecting and characterising the signal from discrete objects embedded in a diffuse background. The approach centres around the evaluation of the posterior distribution for the parameters of the discrete…

The projection predictive variable selection is a decision-theoretically justified Bayesian variable selection approach achieving an outstanding trade-off between predictive performance and sparsity. Its projection problem is not easy to…

Estimating the Shannon entropy of a discrete distribution from which we have only observed a small sample is challenging. Estimating other information-theoretic metrics, such as the Kullback-Leibler divergence between two sparsely sampled…

Bayesian Optimization is methodology used in statistical modelling that utilizes a Gaussian process prior distribution to iteratively update a posterior distribution towards the true distribution of the data. Finding unbiased informative…

In the need for low assumption inferential methods in infinite-dimensional settings, Bayesian adaptive estimation via a prior distribution that does not depend on the regularity of the function to be estimated nor on the sample size is…

Optimization in the Bures-Wasserstein space has been gaining popularity in the machine learning community since it draws connections between variational inference and Wasserstein gradient flows. The variational inference objective function…

There has been much recent interest in modifying Bayesian inference for misspecified models so that it is useful for specific purposes. One popular modified Bayesian inference method is "cutting feedback" which can be used when the model…

In the typical analysis of a data set, a single method is selected for statistical reporting even when equally applicable methods yield very different results. Examples of equally applicable methods can correspond to those of different…

We review typical design problems encountered in the planning of observational studies and propose a unifying framework that allows us to use the same concepts and notation for different problems. In the framework, the design is defined as…

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of…

We consider the parameter estimation problem of a probabilistic generative model prescribed using a natural exponential family of distributions. For this problem, the typical maximum likelihood estimator usually overfits under limited…