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Shrinkage prior are becoming more and more popular in Bayesian modeling for high dimensional sparse problems due to its computational efficiency. Recent works show that a polynomially decaying prior leads to satisfactory posterior…
Substantial advances in Bayesian methods for causal inference have been developed in recent years. We provide an introduction to Bayesian inference for causal effects for practicing statisticians who have some familiarity with Bayesian…
This paper studies a problem of Bayesian parameter estimation for a sequence of scaled counting processes whose weak limit is a Brownian motion with an unknown drift. The main result of the paper is that the limit of the posterior…
The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…
For small area estimation of area-level data, the Fay-Herriot model is extensively used as a model based method. In the Fay-Herriot model, it is conventionally assumed that the sampling variances are known whereas estimators of sampling…
Large Bayesian VARs are now widely used in empirical macroeconomics. One popular shrinkage prior in this setting is the natural conjugate prior as it facilitates posterior simulation and leads to a range of useful analytical results. This…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
We propose a method to improve the efficiency and accuracy of amortized Bayesian inference by leveraging universal symmetries in the joint probabilistic model of parameters and data. In a nutshell, we invert Bayes' theorem and estimate the…
The ubiquity of integrating detectors in imaging and other applications implies that a variety of real-world data are well modeled as Poisson random variables whose means are in turn proportional to an underlying vector-valued signal of…
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…
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…
This paper is concerned with Bayesian inferential methods for data from controlled branching processes that account for model robustness through the use of disparities. Under regularity conditions, we establish that estimators built on…
We develop a novel Empirical Bayes methodology for prediction under check loss in high-dimensional Gaussian models. The check loss is a piecewise linear loss function having differential weights for measuring the amount of underestimation…
Penalized regression methods, such as $L_1$ regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is…
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…
Selecting a subset of variables for linear models remains an active area of research. This paper reviews many of the recent contributions to the Bayesian model selection and shrinkage prior literature. A posterior variable selection summary…
In the value-added literature, it is often claimed that regressing on empirical Bayes shrinkage estimates corrects for the measurement error problem in linear regression. We clarify the conditions needed; we argue that these conditions are…
We investigate the posterior rate of convergence for wavelet shrinkage using a Bayesian approach in general Besov spaces. Instead of studying the Bayesian estimator related to a particular loss function, we focus on the posterior…
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…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…