Related papers: Shrinkage priors for circulant correlation structu…
In a remarkable series of papers beginning in 1956, Charles Stein set the stage for the future development of minimax shrinkage estimators of a multivariate normal mean under quadratic loss. More recently, parallel developments have seen…
Accurate and precise covariance matrices will be important in enabling planned cosmological surveys to detect new physics. Standard methods imply either the need for many N-body simulations in order to obtain an accurate estimate, or a…
This paper addresses the weak instruments problem in linear instrumental variable models from a Bayesian perspective. The new approach has two components. First, a novel predictor-dependent shrinkage prior is developed for the many…
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…
Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…
We develop a general class of Bayesian repulsive Gaussian mixture models that encourage well-separated clusters, aiming at reducing potentially redundant components produced by independent priors for locations (such as the Dirichlet…
During the past decade, shrinkage priors have received much attention in Bayesian analysis of high-dimensional data. This paper establishes the posterior consistency for high-dimensional linear regression with a class of shrinkage priors,…
We consider sparse Bayesian estimation in the classical multivariate linear regression model with $p$ regressors and $q$ response variables. In univariate Bayesian linear regression with a single response $y$, shrinkage priors which can be…
Shrinkage estimation usually reduces variance at the cost of bias. But when we care only about some parameters of a model, I show that we can reduce variance without incurring bias if we have additional information about the distribution of…
An efficient algorithm is proposed for Bayesian model calibration, which is commonly used to estimate the model parameters of non-linear, computationally expensive models using measurement data. The approach is based on Bayesian statistics:…
In high dimensional regression, global local shrinkage priors have gained significant traction for their ability to yield sparse estimates, improve parameter recovery, and support accurate predictive modeling. While recent work has explored…
We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit…
We consider joint inversion for two or more unknown parameters from observational data in the Bayesian framework. Standard approaches often either treat the parameters as independent or impose structural similarity through regularisation…
Frequentist conditions for asymptotic suitability of Bayesian procedures focus on lower bounds for prior mass in Kullback-Leibler neighbourhoods of the data distribution. The goal of this paper is to investigate the flexibility in criteria…
One-step ahead prediction for the multinomial model is considered. The performance of a predictive density is evaluated by the average Kullback-Leibler divergence from the true density to the predictive density. Asymptotic approximations of…
Based on independently distributed $X_1 \sim N_p(\theta_1, \sigma^2_1 I_p)$ and $X_2 \sim N_p(\theta_2, \sigma^2_2 I_p)$, we consider the efficiency of various predictive density estimators for $Y_1 \sim N_p(\theta_1, \sigma^2_Y I_p)$, with…
Simultaneous predictive distributions for independent Poisson observables are investigated. A class of improper prior distributions for Poisson means is introduced. The Bayesian predictive distributions based on priors from the introduced…
Prior distributions for high-dimensional linear regression require specifying a joint distribution for the unobserved regression coefficients, which is inherently difficult. We instead propose a new class of shrinkage priors for linear…
Gaussian distributions are widely used in Bayesian variational inference to approximate intractable posterior densities, but the ability to accommodate skewness can improve approximation accuracy significantly, when data or prior…
Modern approaches to perform Bayesian variable selection rely mostly on the use of shrinkage priors. That said, an ideal shrinkage prior should be adaptive to different signal levels, ensuring that small effects are ruled out, while keeping…