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This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…
Recursive Bayesian inference, in which posterior beliefs are updated in light of accumulating data, is a tool for implementing Bayesian models in applications with streaming and/or very large data sets. As the posterior of one iteration…
We propose a method for estimating the posterior distribution of a standard geostatistical model. After choosing the model formulation and specifying a prior, we use normal mixture densities to approximate the posterior distribution. The…
Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…
We offer a general Bayes theoretic framework to derive posterior contraction rates under a hierarchical prior design: the first-step prior serves to assess the model selection uncertainty, and the second-step prior quantifies the prior…
Optimization constrained by high-fidelity computational models has potential for transformative impact. However, such optimization is frequently unattainable in practice due to the complexity and computational intensity of the model. An…
There is a growing interest in learning how the distribution of a response variable changes with a set of predictors. Bayesian nonparametric dependent mixture models provide a flexible approach to address this goal. However, several…
In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…
We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…
We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…
We propose a novel variational Bayes approach to estimate high-dimensional vector autoregression (VAR) models with hierarchical shrinkage priors. Our approach does not rely on a conventional structural VAR representation of the parameter…
Understanding the relative contributions of environmental, spatial, and temporal processes in shaping species distribution is a central objective in ecology. Bayesian species distribution models (SDMs) offer a flexible framework for this…
As evidenced by various recent and significant papers within the frequentist literature, along with numerous applications in macroeconomics, genomics, and neuroscience, there continues to be substantial interest to understand the…
Structured variational inference constitutes a core methodology in modern statistical applications. Unlike mean-field variational inference, the approximate posterior is assumed to have interdependent structure. We consider the natural…
Bayesian methods have become a popular way to incorporate prior knowledge and a notion of uncertainty into machine learning models. At the same time, the complexity of modern machine learning makes it challenging to comprehend a model's…
This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies…
Bayesian computational strategies for inference can be inefficient in approximating the posterior distribution in models that exhibit some form of periodicity. This is because the probability mass of the marginal posterior distribution of…
Stability selection is a versatile framework for structure estimation and variable selection in high-dimensional setting, primarily grounded in frequentist principles. In this paper, we propose an enhanced methodology that integrates…
In this paper, we propose an infinite-dimensional version of the Stein variational gradient descent (iSVGD) method for solving Bayesian inverse problems. The method can generate approximate samples from posteriors efficiently. Based on the…
We present a nonparametric framework to model a short sequence of probability distributions that vary both due to underlying effects of sequential progression and confounding noise. To distinguish between these two types of variation and…