Related papers: Robust Empirical Bayes Confidence Intervals
Approximate Bayesian computation (ABC) has become an essential tool for the analysis of complex stochastic models when the likelihood function is numerically unavailable. However, the well-established statistical method of empirical…
We propose a new empirical Bayes approach for inference in the $p \gg n$ normal linear model. The novelty is the use of data in the prior in two ways, for centering and regularization. Under suitable sparsity assumptions, we establish a…
Random effects meta-analysis is a widely applied methodology to synthetize research findings of studies in a specific scientific question. Besides estimating the mean effect, an important aim of the meta-analysis is to summarize the…
The construction of the Bayesian credible (confidence) interval for a Poisson observable including both the signal and background with and without systematic uncertainties is presented. Introducing the conditional probability satisfying the…
When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…
Consider a finite sample from an unknown distribution over a countable alphabet. Unobserved events are alphabet symbols which do not appear in the sample. Estimating the probabilities of unobserved events is a basic problem in statistics…
In the present paper, we derive lower bounds for the risk of the nonparametric empirical Bayes estimators. In order to attain the optimal convergence rate, we propose generalization of the linear empirical Bayes estimation method which…
In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…
Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not…
Due to their great flexibility, nonparametric Bayes methods have proven to be a valuable tool for discovering complicated patterns in data. The term "nonparametric Bayes" suggests that these methods inherit model-free operating…
We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use…
Standard blockwise empirical likelihood (BEL) for stationary, weakly dependent time series requires specifying a fixed block length as a tuning parameter for setting confidence regions. This aspect can be difficult and impacts coverage…
We consider a linear regression model, with the parameter of interest a specified linear combination of the regression parameter vector. We suppose that, as a first step, a data-based model selection (e.g. by preliminary hypothesis tests or…
Raking is widely used in categorical data modeling and survey practice but faced with methodological and computational challenges. We develop a Bayesian paradigm for raking by incorporating the marginal constraints as a prior distribution…
The empirical likelihood is a powerful nonparametric tool, that emulates its parametric counterpart -- the parametric likelihood -- preserving many of its large-sample properties. This article tackles the problem of assessing the…
We consider the so-called unfolding problem in experimental high energy physics, where the goal is to estimate the true spectrum of elementary particles given observations distorted by measurement error due to the limited resolution of a…
An empirical Bayes confidence interval has high user demand in many applications. In particular, the second-order empirical Bayes confidence interval, the coverage error of which is of the third order for large number of areas, is widely…
We consider a Bayesian hierarchical version of the normal theory general linear model which is practically relevant in the sense that it is general enough to have many applications and it is not straightforward to sample directly from the…
Empirical likelihood serves as a powerful tool for constructing confidence intervals in nonparametric regression and regression discontinuity designs (RDD). The original empirical likelihood framework can be naturally extended to these…
Models of weak-scale supersymmetry offer viable dark matter (DM) candidates. Their parameter spaces are however rather large and complex, such that pinning down the actual parameter values from experimental data can depend strongly on the…