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This work investigates the sequential hypothesis testing problem with online sensor selection and sensor usage constraints. That is, in a sensor network, the fusion center sequentially acquires samples by selecting one "most informative"…

Applications · Statistics 2016-01-26 Shang Li , Xiaoou Li , Xiaodong Wang , Jingchen Liu

Estimating the probability of the binomial distribution is a basic problem, which appears in almost all introductory statistics courses and is performed frequently in various studies. In some cases, the parameter of interest is a difference…

Computation · Statistics 2024-08-21 Almog Peer , David Azriel

The construction of confidence intervals for the mean of a bounded random variable is a classical problem in statistics with numerous applications in machine learning and virtually all scientific fields. In particular, obtaining the…

Machine Learning · Computer Science 2025-11-12 Václav Voráček , Francesco Orabona

Consider the problem on sequential change-point detection on multiple data streams. We provide the asymptotic lower bounds of the detection delays at all levels of change-point sparsity and we derive a smaller asymptotic lower bound of the…

Statistics Theory · Mathematics 2023-06-02 Jingyan Huang

Many inference problems, such as sequential decision problems like A/B testing, adaptive sampling schemes like bandit selection, are often online in nature. The fundamental problem for online inference is to provide a sequence of confidence…

Statistics Theory · Mathematics 2021-06-07 Arun Kumar Kuchibhotla , Qinqing Zheng

The question of the optimality of Thompson Sampling for solving the stochastic multi-armed bandit problem had been open since 1933. In this paper we answer it positively for the case of Bernoulli rewards by providing the first finite-time…

Machine Learning · Statistics 2012-07-20 Emilie Kaufmann , Nathaniel Korda , Rémi Munos

The problem of sequential anomaly detection is considered, where multiple data sources are monitored in real time and the goal is to identify the "anomalous" ones among them, when it is not possible to sample all sources at all times. A…

Statistics Theory · Mathematics 2022-05-23 Aristomenis Tsopelakos , Georgios Fellouris

Without imposing prior distributional knowledge underlying multivariate time series of interest, we propose a nonparametric change-point detection approach to estimate the number of change points and their locations along the temporal axis.…

Methodology · Statistics 2021-05-13 Xiaodong Wang , Fushing Hsieh

Real numbers from the interval [0, 1] are randomly selected with uniform distribution. There are $n$ of them and they are revealed one by one. However, we do not know their values but only their relative ranks. We want to stop on recently…

Combinatorics · Mathematics 2019-04-30 Ewa M. Kubicka , Grzegorz Kubicki , Małgorzata Kuchta , Małgorzata Sulkowska

It is a common contention that it is an ``impossible mission'' to exactly determine the minimum sample size for the estimation of a binomial parameter with prescribed margin of error and confidence level. In this paper, we investigate such…

Statistics Theory · Mathematics 2007-08-02 Xinjia Chen

Change point detection plays a fundamental role in many real-world applications, where the goal is to analyze and monitor the behaviour of a data stream. In this paper, we study change detection in binary streams. To this end, we use a…

Machine Learning · Computer Science 2023-01-24 Nikolaj Tatti

We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…

Machine Learning · Statistics 2020-09-22 Miaoyan Wang , Lexin Li

Discovery problems often require deciding whether additional sampling is needed to detect all categories whose prevalence exceeds a prespecified threshold. We study this question under a Bernoulli product (incidence) model, where categories…

Methodology · Statistics 2026-01-29 Alessandro Colombi , Mario Beraha , Amichai Painsky , Stefano Favaro

This paper revisits the classical problem of interval estimation of a binomial proportion under Huber contamination. Our main result derives the rate of optimal interval length when the contamination proportion is unknown under a local…

Statistics Theory · Mathematics 2026-01-13 Minjun Cho , Yuetian Luo , Chao Gao

Given an initial (resp., terminal) probability measure $\mu$ (resp., $\nu$) on $\mathbb{R}^d$, we characterize those optimal stopping times $\tau$ that maximize or minimize the functional $\mathbb{E} |B_0 - B_\tau|^{\alpha}$, $\alpha > 0$,…

Probability · Mathematics 2017-11-09 Nassif Ghoussoub , Young-Heon Kim , Tongseok Lim

Sequential Bayesian experimental design typically assumes that the number of experiments is fixed before data collection begins. In practical campaigns, however, experimentation may need to terminate early because additional measurements…

Methodology · Statistics 2026-05-29 Chen Cheng , Xun Huan

The estimation of a probability p from repeated Bernoulli trials is considered in this paper. A sequential approach is followed, using a simple stopping rule. A closed-form expression and an upper bound are obtained for the mean absolute…

Statistics Theory · Mathematics 2018-12-19 Luis Mendo

In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level,…

Statistics Theory · Mathematics 2013-11-05 Xinjia Chen

We treat the statistical inference problems in which one needs to detect and estimate simultaneously using as small number of samples as possible. Conventional methods treat the detection and estimation subproblems separately, ignoring the…

Applications · Statistics 2014-11-07 Yasin Yilmaz , Shang Li , Xiaodong Wang

A novel quickest detection setting is proposed which is a generalization of the well-known Bayesian change-point detection model. Suppose \{(X_i,Y_i)\}_{i\geq 1} is a sequence of pairs of random variables, and that S is a stopping time with…

Statistics Theory · Mathematics 2016-11-17 Urs Niesen , Aslan Tchamkerten