相关论文: On the behavior of Bayesian credible intervals for…

We consider the problem of inference on the signs of $n>1$ parameters. We aim to provide $1-\alpha$ post-hoc confidence bounds on the number of positive and negative (or non-positive) parameters. The guarantee is simultaneous, for all…

This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A lower bound on the Bayes risk not only serves as a lower bound…

We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy. First, we prove that for any $\alpha \le O(1)$, estimating the…

Consider the problem of nonparametric estimation of an unknown $\beta$-H\"older smooth density $p_{XY}$ at a given point, where $X$ and $Y$ are both $d$ dimensional. An infinite sequence of i.i.d.\ samples $(X_i,Y_i)$ are generated…

We investigate the credible sets and marginal credible intervals resulting from the horseshoe prior in the sparse multivariate normal means model. We do so in an adaptive setting without assuming knowledge of the sparsity level (number of…

The choice of tuning parameters in Bayesian variable selection is a critical problem in modern statistics. In particular, for Bayesian linear regression with non-local priors, the scale parameter in the non-local prior density is an…

Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…

The Na\"ive Mean Field (NMF) approximation is widely employed in modern Machine Learning due to the huge computational gains it bestows on the statistician. Despite its popularity in practice, theoretical guarantees for high-dimensional…

High-dimensional Bayesian procedures often exhibit behavior that is effectively low dimensional, even when the ambient parameter space is large or infinite-dimensional. This phenomenon underlies the success of shrinkage priors,…

Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…

What, if anything, should a frequentist say about a single realized confidence interval (CI) and its chance of having covered the parameter? Jerzy Neyman's original answer was to refuse any nondegenerate probability for coverage ex post…

In Neyman's original formulation, a 1-alpha confidence interval procedure is justified by its long-run coverage properties, and a single realized interval is to be described only by the slogan that it either covers the parameter or it does…

This paper considers estimation of the predictive density for a normal linear model with unknown variance under alpha-divergence loss for -1 <= alpha <= 1. We first give a general canonical form for the problem, and then give general…

We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. When the input…

Empirical Bayes small area estimation based on the well-known Fay-Herriot model may produce unreliable estimates when outlying areas exist. Existing robust methods against outliers or model misspecification are generally inefficient when…

We consider a linear regression model with regression parameter beta =(beta_1, ..., beta_p) and independent and identically N(0, sigma^2)distributed errors. Suppose that the parameter of interest is theta = a^T beta where a is a specified…

In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained.…

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

The normal-normal hierarchical model (NNHM) constitutes a simple and widely used framework for meta-analysis. In the common case of only few studies contributing to the meta-analysis, standard approaches to inference tend to perform poorly,…

Small area estimation (SAE) improves estimates for local communities or groups, such as counties, neighborhoods, or demographic subgroups, when data are insufficient for each area. This is important for targeting local resources and…