Related papers: Leveraging Self-Consistency for Data-Efficient Amo…
To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…
We propose a general solution to the problem of robust Bayesian inference in complex settings where outliers may be present. In practice, the automation of robust Bayesian analyses is important in the many applications involving large and…
Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…
Bayesian decision theory outlines a rigorous framework for making optimal decisions based on maximizing expected utility over a model posterior. However, practitioners often do not have access to the full posterior and resort to approximate…
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…
We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions indexed by a hyperparameter that quantifies…
Shape restrictions such as monotonicity on functions often arise naturally in statistical modeling. We consider a Bayesian approach to the problem of estimation of a monotone regression function and testing for monotonicity. We construct a…
Quantile regression is often used when a comprehensive relationship between a response variable and one or more explanatory variables is desired. The traditional frequentists' approach to quantile regression has been well developed around…
Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…
Negative binomial regression is commonly employed to analyze overdispersed count data. With small to moderate sample sizes, the maximum likelihood estimator of the dispersion parameter may be subject to a significant bias, that in turn…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
In the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints. For instance, when examining three group means $\{ \mu_1, \mu_2, \mu_3\}$ through an analysis of variance…
The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…
Approximate Bayesian inference typically revolves around computing the posterior parameter distribution. In practice, however, the main object of interest is often a model's predictions rather than its parameters. In this work, we propose…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes…
Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…
Supervised topic models with a logistic likelihood have two issues that potentially limit their practical use: 1) response variables are usually over-weighted by document word counts; and 2) existing variational inference methods make…
Current approaches to amortizing Bayesian inference focus solely on approximating the posterior distribution. Typically, this approximation is, in turn, used to calculate expectations for one or more target functions - a computational…
It is generally believed that ensemble approaches, which combine multiple algorithms or models, can outperform any single algorithm at machine learning tasks, such as prediction. In this paper, we propose Bayesian convex and linear…