Related papers: Ideal Bayesian Spatial Adaptation

In this work, we focus on variational Bayesian inference on the sparse Deep Neural Network (DNN) modeled under a class of spike-and-slab priors. Given a pre-specified sparse DNN structure, the corresponding variational posterior contraction…

High-dimensional spatially correlated covariates are common in regression models encountered in environmental sciences and other fields. In such models, the regression coefficients often exhibit a sparse structure with spatial dependence.…

Due to spatial dependence -- often characterized as complex and non-linear -- model misspecification is a prevalent and critical issue in spatial data analysis and prediction. As the data, and thus model performance, is heterogeneous,…

Spatial modelling often uses Gaussian random fields to capture the stochastic nature of studied phenomena. However, this approach incurs significant computational burdens (O(n3)), primarily due to covariance matrix computations. In this…

Due to developments in instruments and computers, functional observations are increasingly popular. However, effective methodologies for flexibly estimating the underlying trends with valid uncertainty quantification for a sequence of…

Bayesian neural networks (BNNs) have received an increased interest in the last years. In BNNs, a complete posterior distribution of the unknown weight and bias parameters of the network is produced during the training stage. This…

Conditional autoregressive (CAR) models are commonly used to capture spatial correlation in areal unit data, and are typically specified as a prior distribution for a set of random effects, as part of a hierarchical Bayesian model. The…

We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building upon a global-local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are…

In the density estimation model, the question of adaptive inference using P\'olya tree-type prior distributions is considered. A class of prior densities having a tree structure, called spike-and-slab P\'olya trees, is introduced. For this…

In this work we propose and analyze a Hessian-based adaptive sparse quadrature to compute infinite-dimensional integrals with respect to the posterior distribution in the context of Bayesian inverse problems with Gaussian prior. Due to the…

Bayesian analysis of functions and curves is considered, where warping and other geometrical transformations are often required for meaningful comparisons. We focus on two applications involving the classification of mouse vertebrae shape…

This article introduces two absolutely continuous global-local shrinkage priors to enable stochastic variable selection in the context of high-dimensional matrix exponential spatial specifications. Existing approaches as a means to dealing…

Despite its long history, Bayesian neural networks (BNNs) and variational training remain underused in practice: standard Gaussian posteriors misalign with network geometry, KL terms can be brittle in high dimensions, and implementations…

Quantifying spatial and/or temporal associations in multivariate geolocated data of different types is achievable via spatial random effects in a Bayesian hierarchical model, but severe computational bottlenecks arise when spatial…

Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without…

We begin by introducing a class of conditional density estimators based on local polynomial techniques. The estimators are boundary adaptive and easy to implement. We then study the (pointwise and) uniform statistical properties of the…

Achieving robust uncertainty quantification for deep neural networks represents an important requirement in many real-world applications of deep learning such as medical imaging where it is necessary to assess the reliability of a neural…

Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…

We study the generalization error of randomized learning algorithms -- focusing on stochastic gradient descent (SGD) -- using a novel combination of PAC-Bayes and algorithmic stability. Importantly, our generalization bounds hold for all…

We present a Bayesian nonparametric model for conditional distribution estimation using Bayesian additive regression trees (BART). The generative model we use is based on rejection sampling from a base model. Typical of BART models, our…