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In wavelet shrinkage and thresholding, most of the standard techniques do not consider information that wavelet coefficients might be bounded, although information about bounded energy in signals can be readily available. To address this,…

Methodology · Statistics 2020-11-12 Alex Rodrigo dos Santos Sousa , Nancy Lopes Garcia , Branislav Vidakovic

Bayesian deep learning approaches assume model parameters to be latent random variables and infer posterior distributions to quantify uncertainty, increase safety and trust, and prevent overconfident and unpredictable behavior. However,…

Machine Learning · Computer Science 2023-07-13 Jihao Andreas Lin , Joe Watson , Pascal Klink , Jan Peters

In inference problems involving a multi-dimensional parameter $\theta$, it is often natural to consider decision rules that have a risk which is invariant under some group $G$ of permutations of $\theta$. We show that this implies that the…

Methodology · Statistics 2014-07-01 Erik van Zwet

The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…

Statistics Theory · Mathematics 2014-07-03 Antonio Lijoi , Bernardo Nipoti , Igor Prünster

Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian…

Methodology · Statistics 2022-01-12 Takuo Matsubara , Jeremias Knoblauch , François-Xavier Briol , Chris. J. Oates

Background and Objective: Wilson statistics describe well the power spectrum of proteins at high frequencies. Therefore, it has found several applications in structural biology, e.g., it is the basis for sharpening steps used in cryogenic…

Quantitative Methods · Quantitative Biology 2022-05-03 Marc Aurèle Gilles , Amit Singer

In this work, Bayesian inversion with global-local forwards models is used to identify the parameters based on hydraulic fractures in porous media. It is well-known that using Bayesian inversion to identify material parameters is…

Numerical Analysis · Mathematics 2023-04-11 Nima Noii , Thomas Wick , Amirreza Khodadadian

It can be important in Bayesian analyses of complex models to construct informative prior distributions which reflect knowledge external to the data at hand. Nevertheless, how much prior information an analyst can elicit from an expert will…

Applications · Statistics 2017-11-10 Xueou Wang , David J. Nott , C. C. Drovandi , Kerrie Mengersen , Michael Evans

We consider the classical problems of estimating the mean of an $n$-dimensional normally (with identity covariance matrix) or Poisson distributed vector under the squared loss. In a Bayesian setting the optimal estimator is given by the…

Statistics Theory · Mathematics 2021-09-13 Yury Polyanskiy , Yihong Wu

Bayesian neural networks (BNNs) treat neural network weights as random variables, which aim to provide posterior uncertainty estimates and avoid overfitting by performing inference on the posterior weights. However, the selection of…

Machine Learning · Computer Science 2025-05-27 Tsai Hor Chan , Dora Yan Zhang , Guosheng Yin , Lequan Yu

We develop a Bayesian tree ensemble model to estimate heterogeneous treatment effects in censored survival data with high-dimensional covariates. Instead of imposing sparsity through the tree structure, we place a horseshoe prior directly…

Methodology · Statistics 2026-05-08 Tijn Jacobs , Wessel N. van Wieringen , Stéphanie L. van der Pas

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

Statistics Theory · Mathematics 2020-02-04 Vladimir Spokoiny

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…

Machine Learning · Computer Science 2019-04-03 Konstantin Posch , Jürgen Pilz

We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the…

Statistics Theory · Mathematics 2014-07-28 Naveen Naidu Narisetty , Xuming He

Bayesian neural networks provide a direct and natural way to extend standard deep neural networks to support probabilistic deep learning through the use of probabilistic layers that, traditionally, encode weight (and bias) uncertainty. In…

Machine Learning · Computer Science 2021-07-16 Daniel T. Chang

Reference priors are theoretically attractive for the analysis of geostatistical data since they enable automatic Bayesian analysis and have desirable Bayesian and frequentist properties. But their use is hindered by computational hurdles…

Methodology · Statistics 2022-01-27 Victor De Oliveira , Zifei Han

Sparse deep neural networks have proven to be efficient for predictive model building in large-scale studies. Although several works have studied theoretical and numerical properties of sparse neural architectures, they have primarily…

Machine Learning · Statistics 2023-09-18 Sanket Jantre , Shrijita Bhattacharya , Tapabrata Maiti

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

Statistics Theory · Mathematics 2025-11-25 Sayantan Banerjee , Ismaël Castillo , Subhashis Ghosal

The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…

Machine Learning · Statistics 2023-10-09 Eliezer de Souza da Silva , Tomasz Kuśmierczyk , Marcelo Hartmann , Arto Klami

We investigate predictive densities for multivariate normal models with unknown mean vectors and known covariance matrices. Bayesian predictive densities based on shrinkage priors often have complex representations, although they are…

Methodology · Statistics 2022-12-08 Michiko Okudo , Fumiyasu Komaki