Related papers: Asymptotically minimax empirical Bayes estimation …
The objective of the present paper is to develop a minimax theory for the varying coefficient model in a non-asymptotic setting. We consider a high-dimensional sparse varying coefficient model where only few of the covariates are present…
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…
This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…
We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…
In an indirect Gaussian sequence space model lower and upper bounds are derived for the concentration rate of the posterior distribution of the parameter of interest shrinking to the parameter value $\theta^\circ$ that generates the data.…
This article studies the asymptotic properties of Bayesian or frequentist estimators of a vector of parameters related to structural properties of sequences of graphs. The estimators studied originate from a particular class of graphex…
Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated…
We consider the horseshoe estimator due to Carvalho, Polson and Scott (2010) for the multivariate normal mean model in the situation that the mean vector is sparse in the nearly black sense. We assume the frequentist framework where the…
Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…
It is well known that if the power spectral density of a continuous time stationary stochastic process does not have a compact support, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum…
Evaluating treatments received by one population for application to a different target population of scientific interest is a central problem in causal inference from observational studies. We study the minimax linear estimator of the…
Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…
We consider the problem of predictive density estimation under Kullback-Leibler loss in a high-dimensional Gaussian model with exact sparsity constraints on the location parameters. We study the first order asymptotic minimax risk of Bayes…
As for other latent-variable problems, exact Bayesian analysis is typically not practicable for mixture problems and approximate methods have been developed. Variational Bayes tends to produce approximate posterior distributions for…
Bayesian approaches for learning deep neural networks (BNN) have been received much attention and successfully applied to various applications. Particularly, BNNs have the merit of having better generalization ability as well as better…
Multi-level normal hierarchical models, also interpreted as mixed effects models, play an important role in developing statistical theory in multi-parameter estimation for a wide range of applications. In this article, we propose a novel…
This paper introduces a quasi-Bayesian method that integrates frequentist nonparametric estimation with Bayesian inference in a two-stage process. Applied to an endogenous discrete choice model, the approach first uses kernel or sieve…
Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always…
In some applied scenarios, the availability of complete data is restricted, often due to privacy concerns; only aggregated, robust and inefficient statistics derived from the data are made accessible. These robust statistics are not…
We consider Bayesian inference of signals with vector-valued entries. Extending concentration techniques from the mathematical physics of spin glasses, we show that the matrix-valued minimum mean-square error concentrates when the size of…