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This work concerns developing communication- and computation-efficient methods for large-scale multiple testing over networks, which is of interest to many practical applications. We take an asymptotic approach and propose two methods,…

Methodology · Statistics 2024-03-19 Mehrdad Pournaderi , Yu Xiang

This paper proposes a max-test for testing (possibly infinitely) many zero parameter restrictions in an extremum estimation framework. The test statistic is formed by estimating key parameters one at a time based on many empirical loss…

Statistics Theory · Mathematics 2022-04-12 Jonathan B. Hill

In high-dimensional settings, sparse structures are critical for efficiency in term of memory and computation complexity. For a linear system, to find the sparsest solution provided with an over-complete dictionary of features directly is…

Machine Learning · Statistics 2020-07-09 Yiping Jiang , Tianshi Chen

New problems arise when the standard theory of joint detection and estimation is applied to a set of signals drawn from a continuous family; decision thresholds must be determined as a function of the continuous parameter x characterizing…

Statistics Theory · Mathematics 2014-07-17 D. Michael Milder , Robert G. Lindgren , Morris M. Berman

The main contribution of this paper is a mathematical definition of statistical sparsity, which is expressed as a limiting property of a sequence of probability distributions. The limit is characterized by an exceedance measure~$H$ and a…

Methodology · Statistics 2018-05-24 Peter McCullagh , Nicholas Polson

We study an optimal process control problem with multiple assignable causes. The process is initially in-control but is subject to random transition to one of multiple out-of-control states due to assignable causes. The objective is to find…

Optimization and Control · Mathematics 2012-12-12 Jue Wang , Chi-Guhn Lee

We study a Bayesian binary sequential hypothesis testing problem with multiple large language models (LLMs). Each LLM $j$ has per-query cost $c_j>0$, random waiting time with mean $\mu_j>0$ and sub-Gaussian tails, and \emph{asymmetric}…

Data Structures and Algorithms · Computer Science 2026-04-03 Guokai Li , Alys Liang , Mo Liu , Murray Lei , Stefanus Jasin , Fenghua Yang , Preet Baxi

Performance bounds for parameter estimation play a crucial role in statistical signal processing theory and applications. Two widely recognized bounds are the Cram\'{e}r-Rao bound (CRB) in the non-Bayesian framework, and the Bayesian CRB…

Information Theory · Computer Science 2023-11-27 Ori Aharon , Joseph Tabrikian

The problem of simultaneously testing the marginal distributions of sequentially monitored, independent data streams is considered. The decisions for the various testing problems can be made at different times, using data from all streams,…

Methodology · Statistics 2023-04-21 Yiming Xing , Georgios Fellouris

We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions indexed by a hyperparameter that quantifies…

Statistics Theory · Mathematics 2013-05-30 B. T. Knapik , B. T. Szabó , A. W. van der Vaart , J. H. van Zanten

We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…

Methodology · Statistics 2025-02-04 Aihua Li , Surya T. Tokdar , Jason Xu

Design of experiments has traditionally relied on the frequentist hypothesis testing framework where the optimal size of the experiment is specified as the minimum sample size that guarantees a required level of power. Sample size…

Methodology · Statistics 2025-08-07 Shirin Golchi , Luke Hagar

Bayesian optimization (BO) is increasingly employed in critical applications to find the optimal design with minimal cost. While BO is known for its sample efficiency, relying solely on costly high-fidelity data can still result in high…

Artificial Intelligence · Computer Science 2025-03-25 Zahra Zanjani Foumani , Ramin Bostanabad

In this paper, we consider the problem of noiseless non-adaptive probabilistic group testing, in which the goal is high-probability recovery of the defective set. We show that in the case of $n$ items among which $k$ are defective, the…

Information Theory · Computer Science 2021-07-30 Wei Heng Bay , Eric Price , Jonathan Scarlett

This study establishes the consistency of Bayesian adaptive testing methods under the Rasch model, addressing a gap in the literature on their large-sample guarantees. Although Bayesian approaches are recognized for their finite-sample…

Methodology · Statistics 2024-12-11 Hau-Hung Yang , Chia-Min Wei , Yu-Chang Chen

A classical problem in digital communications is to evaluate the symbol error probability (SEP) and bit error probability (BEP) of a multidimensional constellation over an additive white Gaussian noise channel. In this paper, we revisit…

Information Theory · Computer Science 2024-01-25 Alex Alvarado , Erik Agrell , Fredrik Brännström

Approximate Bayesian computation (ABC) is a popular technique for approximating likelihoods and is often used in parameter estimation when the likelihood functions are analytically intractable. Although the use of ABC is widespread in many…

Statistics Theory · Mathematics 2011-03-29 Thomas A. Dean , Sumeetpal S. Singh , Ajay Jasra , Gareth W. Peters

The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second, the probabilities of at least $k_1$…

Statistics Theory · Mathematics 2019-02-18 Yanglei Song , Georgios Fellouris

We study asymptotic behaviors of Bayes type estimators and give sufficient conditions to obtain asymptotic limit distribution of estimation error. We assume polynomial type large deviation inequalities and prove asymptotic equivalence of…

Statistics Theory · Mathematics 2013-12-31 Teppei Ogihara

This paper demonstrates how new principles of compressed sensing, namely asymptotic incoherence, asymptotic sparsity and multilevel sampling, can be utilised to better understand underlying phenomena in practical compressed sensing and…

Functional Analysis · Mathematics 2014-07-08 Bogdan Roman , Anders Hansen , Ben Adcock