Sequential Analysis-Design Methods and Applications最新文献

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Bayesian sequential joint detection and estimation under multiple hypotheses 多假设下贝叶斯序列联合检测与估计

IF 0.8 4区数学 Q3 Mathematics

Sequential Analysis-Design Methods and Applications

Pub Date : 2020-03-27 DOI: 10.1080/07474946.2022.2043053

Dominik Reinhard, Michael Fauss, A. Zoubir

Abstract We consider the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution. This problem is investigated in a sequential setup under mild assumptions on the underlying random process. The optimal method minimizes the expected number of samples while ensuring that the average detection/estimation errors do not exceed a certain level. After converting the constrained problem to an unconstrained one, we characterize the general solution by a nonlinear Bellman equation, which is parameterized by a set of cost coefficients. A strong connection between the derivatives of the cost function with respect to the coefficients and the detection/estimation errors of the sequential procedure is derived. Based on this fundamental property, we further show that for suitably chosen cost coefficients the solutions of the constrained and the unconstrained problem coincide. We present two approaches to finding the optimal coefficients. For the first approach, the final optimization problem is converted into a linear program, whereas the second approach solves it with a projected gradient ascent. To illustrate the theoretical results, we consider two problems for which the optimal schemes are designed numerically. Using Monte Carlo simulations, it is validated that the numerical results agree with the theory.

摘要我们考虑联合检验多个假设并估计潜在分布的随机参数的问题。在对潜在随机过程的温和假设下，在顺序设置中研究了这个问题。最优方法最小化期望的样本数量，同时确保平均检测/估计误差不超过特定水平。在将约束问题转化为无约束问题后，我们用一个非线性Bellman方程来刻画一般解，该方程由一组成本系数参数化。导出了成本函数相对于系数的导数与序列过程的检测/估计误差之间的强联系。基于这一基本性质，我们进一步证明了对于适当选择的成本系数，约束问题和无约束问题的解是一致的。我们提出了两种寻找最优系数的方法。对于第一种方法，将最终的优化问题转换为线性规划，而第二种方法通过投影梯度上升来解决它。为了说明理论结果，我们考虑了两个问题，并对其进行了数值设计。通过蒙特卡洛模拟，验证了数值结果与理论的一致性。

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引用次数: 3

Detecting changes in the second moment structure of high-dimensional sensor-type data in a K-sample setting 在K样本设置中检测高维传感器类型数据的二阶矩结构的变化

IF 0.8 4区数学 Q3 Mathematics

Sequential Analysis-Design Methods and Applications

Pub Date : 2020-01-15 DOI: 10.1080/07474946.2020.1823192

Nils Mause, A. Steland

Abstract The K sample problem for high-dimensional vector time series is studied, especially focusing on sensor data streams, in order to analyze the second moment structure and detect changes across samples and/or across variables cumulated sum (CUSUM) statistics of bilinear forms of the sample covariance matrix. In this model, K independent vector time series are observed over a time span which may correspond to K sensors (locations) yielding d-dimensional data as well as K locations where d sensors emit univariate data. Unequal sample sizes are considered as arising when the sampling rate of the sensors differs. We provide large-sample approximations and two related change point statistics, a sum of squares and a pooled variance statistic. The resulting procedures are investigated by simulations and illustrated by analyzing a real data set.

摘要研究了高维向量时间序列的K样本问题，特别是关注传感器数据流，以分析二阶矩结构，并检测样本协方差矩阵双线性形式的样本间和/或变量间累积和（CUSUM）统计量的变化。在该模型中，在一个时间跨度上观察到K个独立的矢量时间序列，该时间跨度可以对应于产生d维数据的K个传感器（位置）以及d个传感器发射单变量数据的K位置。当传感器的采样率不同时，会出现样本大小不等的情况。我们提供了大样本近似和两个相关的变化点统计，一个平方和和和一个合并方差统计。通过仿真研究了产生的过程，并通过分析真实数据集进行了说明。

引用次数: 2

Sequential algorithms for moving anomaly detection in networks 网络中运动异常检测的顺序算法

IF 0.8 4区数学 Q3 Mathematics

Sequential Analysis-Design Methods and Applications

Pub Date : 2020-01-02 DOI: 10.1080/07474946.2020.1726678

Georgios Rovatsos, Shaofeng Zou, V. Veeravalli

Abstract The problem of quickest moving anomaly detection in networks is studied. Initially, the observations are generated according to a prechange distribution. At some unknown but deterministic time, an anomaly emerges in the network. At each time instant, one node is affected by the anomaly and receives data from a post-change distribution. The anomaly moves across the network, and the node that it affects changes with time. However, the trajectory of the moving anomaly is assumed to be unknown. A discrete-time Markov chain is employed to model the unknown trajectory of the moving anomaly in the network. A windowed generalized likelihood ratio–based test is constructed and is shown to be asymptotically optimal. Other detection algorithms including the dynamic Shiryaev-Roberts test, a quickest change detection algorithm with recursive change point estimation, and a mixture cumulative sum (CUSUM) algorithm are also developed for this problem. Lower bounds on the mean time to false alarm are developed. Numerical results are further provided to compare their performances.

摘要研究了网络中移动最快的异常检测问题。最初，观测值是根据变化前的分布生成的。在某个未知但确定的时间，网络中出现异常。在每个时刻，一个节点都会受到异常的影响，并从变化后的分布中接收数据。异常在网络中移动，它影响的节点会随着时间的推移而变化。然而，假设移动异常的轨迹是未知的。采用离散时间马尔可夫链对网络中移动异常的未知轨迹进行建模。构造了一个基于窗口广义似然比的检验，证明了它是渐近最优的。针对这个问题，还开发了其他检测算法，包括动态Shiryaev-Roberts检验、具有递归变化点估计的最快变化检测算法和混合累积和（CUSUM）算法。建立了平均虚警时间的下限。进一步提供了数值结果来比较它们的性能。

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引用次数: 16

CBM for testing multiple hypotheses with directional alternatives in sequential experiments CBM用于序列实验中具有方向选择的多个假设的检验

IF 0.8 4区数学 Q3 Mathematics

Sequential Analysis-Design Methods and Applications

Pub Date : 2020-01-02 DOI: 10.1080/07474946.2020.1727166

K. Kachiashvili, J. K. Kachiashvili, I. Prangishvili

Abstract Constrained Bayesian methods (CBMs) and the concept of false discovery rates (FDRs) for testing directional hypotheses are considered in this article. It is shown that the direct application of CBM allows us to control FDR on the desired level for both one set of directional hypotheses and a multiple case when we consider () sets of directional hypotheses. When guaranteeing restriction on the desired level, a Bayesian sequential method can be applied, the stopping rules of which are proper and the sequential scheme for making a decision strongly controls the mixed directional FDR. Computational results of concrete examples confirm the correctness of the theoretical outcomes.

摘要本文考虑了用于检验方向性假设的约束贝叶斯方法（CBM）和错误发现率（FDRs）的概念。研究表明，当我们考虑（）组方向假设时，CBM的直接应用使我们能够将一组方向假设和多个情况的FDR控制在所需水平上。当保证对期望水平的限制时，可以应用贝叶斯序列方法，其停止规则是适当的，并且用于做出决策的序列方案强烈地控制混合方向FDR。具体算例的计算结果验证了理论结果的正确性。

引用次数: 2

Editor’s Note 编者按

IF 0.8 4区数学 Q3 Mathematics

Sequential Analysis-Design Methods and Applications

Pub Date : 2020-01-02 DOI: 10.1080/07474946.2020.1726688

Analúcia Danilevicz Pereira

引用次数: 0

Exponential inequalities for Mann’s stochastic algorithm Mann随机算法的指数不等式

IF 0.8 4区数学 Q3 Mathematics

Sequential Analysis-Design Methods and Applications

Pub Date : 2020-01-02 DOI: 10.1080/07474946.2020.1726681

Chahira Allouti, Bahia Barache, A. Dahmani

Abstract In this article, we investigate the problem of approximating the fixed point for some function using a Mann iterative process with random errors. After establishing some exponential inequalities, we prove the complete convergence of Mann’s algorithm toward the fixed point and deduce a confidence interval for this one. In addition, we establish the convergence rate of Mann’s algorithm. Several numerical examples are sketched to illustrate the performance of the proposed algorithm.

摘要在本文中，我们研究了使用具有随机误差的Mann迭代过程来逼近某个函数的不动点的问题。在建立了一些指数不等式后，我们证明了Mann算法向不动点的完全收敛性，并推导出该算法的置信区间。此外，我们还建立了Mann算法的收敛速度。通过几个算例说明了该算法的性能。

引用次数: 0

Sequential Tests of Multiple Hypotheses Controlling False Discovery and Nondiscovery Rates. 控制错误发现率和未发现率的多假设序列检验。

IF 0.8 4区数学 Q3 Mathematics

Sequential Analysis-Design Methods and Applications

Pub Date : 2020-01-01 Epub Date: 2020-05-13 DOI: 10.1080/07474946.2020.1726686

Jay Bartroff, Jinlin Song

We propose a general and flexible procedure for testing multiple hypotheses about sequential (or streaming) data that simultaneously controls both the false discovery rate (FDR) and false nondiscovery rate (FNR) under minimal assumptions about the data streams which may differ in distribution, dimension, and be dependent. All that is needed is a test statistic for each data stream that controls its conventional type I and II error probabilities, and no information or assumptions are required about the joint distribution of the statistics or data streams. The procedure can be used with sequential, group sequential, truncated, or other sampling schemes. The procedure is a natural extension of Benjamini and Hochberg's (1995) widely-used fixed sample size procedure to the domain of sequential data, with the added benefit of simultaneous FDR and FNR control that sequential sampling affords. We prove the procedure's error control and give some tips for implementation in commonly encountered testing situations.

我们提出了一个通用的和灵活的过程来测试关于序列(或流)数据的多个假设，同时控制错误发现率(FDR)和错误未发现率(FNR)，在最小的假设下，数据流可能在分布、维度和依赖性上不同。所需要的只是每个数据流的测试统计量，该统计量控制其常规类型I和II的错误概率，并且不需要关于统计量或数据流的联合分布的信息或假设。该程序可用于顺序，组顺序，截断或其他抽样方案。该过程是Benjamini和Hochberg(1995)广泛使用的固定样本量过程在顺序数据领域的自然扩展，具有顺序采样提供的同时FDR和FNR控制的附加好处。证明了该程序的误差控制，并给出了一些常见测试情况下的实施提示。

引用次数: 15

Sequential controlled sensing for composite multihypothesis testing 序列控制传感复合多假设检验

IF 0.8 4区数学 Q3 Mathematics

Sequential Analysis-Design Methods and Applications

Pub Date : 2019-10-24 DOI: 10.1080/07474946.2021.1912525

Aditya Deshmukh, S. Bhashyam, V. Veeravalli

Abstract The problem of multihypothesis testing with controlled sensing of observations is considered. The distribution of observations collected under each control is assumed to follow a single-parameter exponential family distribution. The goal is to design a policy to find the true hypothesis with minimum expected delay while ensuring that the probability of error is below a given constraint. The decision-maker can reduce the delay by intelligently choosing the control for observation collection in each time slot. A policy for this problem is derived that satisfies given constraints on the error probability, and it is shown that this policy is asymptotically optimal in the sense that it asymptotically achieves an information-theoretic lower bound on the expected delay. Numerical results are provided that illustrate an application of the policy to medical diagnostic inference.

摘要研究了具有观测值控制感知的多假设检验问题。假设在每个控制下收集的观测值的分布遵循单参数指数族分布。目标是设计一个策略，以最小的期望延迟找到真实的假设，同时确保错误概率低于给定的约束。决策者可以通过智能选择每个时隙的观测采集控制来减少延迟。对该问题导出了一个满足给定误差概率约束的策略，并证明了该策略是渐近最优的，因为它渐近地达到了期望延迟的信息论下界。数值结果说明了该策略在医学诊断推理中的应用。

引用次数: 11

High-confidence nonparametric fixed-width uncertainty intervals and applications to projected high-dimensional data and common mean estimation 高置信度非参数固定宽度不确定性区间及其在投影高维数据和共同均值估计中的应用

IF 0.8 4区数学 Q3 Mathematics

Sequential Analysis-Design Methods and Applications

Pub Date : 2019-10-07 DOI: 10.1080/07474946.2021.1847966

A. Steland, Yuan-Tsung Chang

Abstract Nonparametric two-stage procedures to construct fixed-width confidence intervals are studied to quantify uncertainty. It is shown that the validity of the random central limit theorem (RCLT) accompanied by a consistent and asymptotically unbiased estimator of the asymptotic variance already guarantees consistency and first-order as well as second-order efficiency of the two-stage procedures. This holds under the common asymptotics where the length of the confidence interval tends toward 0 as well as under the novel proposed high-confidence asymptotics where the confidence level tends toward 1. The approach is motivated by and applicable to data analysis from distributed big data with nonnegligible costs of data queries. The following problems are discussed: Fixed-width intervals for the mean, for a projection when observing high-dimensional data, and for the common mean when using nonlinear common mean estimators under order constraints. The procedures are investigated by simulations and illustrated by a real data analysis.

摘要研究了构造固定宽度置信区间的非参数两阶段程序，以量化不确定性。结果表明，随机中心极限定理（RCLT）伴随着渐近方差的一致和渐近无偏估计量的有效性已经保证了两阶段过程的一致性和一阶和二阶效率。这在置信区间长度趋向于0的常见渐近线下以及在置信水平趋向于1的新提出的高置信度渐近线中都成立。该方法受分布式大数据的启发，适用于具有不可忽略的数据查询成本的数据分析。讨论了以下问题：均值的固定宽度区间，观测高维数据时的投影，以及在阶约束下使用非线性共同均值估计量时的共同均值。通过模拟对程序进行了研究，并通过实际数据分析进行了说明。

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引用次数: 2

Sequential minimum risk point estimation (MRPE) methodology for a normal mean under Linex loss plus sampling cost: First-order and second-order asymptotics Linex损失加采样代价下正态均值的序贯最小风险点估计方法:一阶和二阶渐近性

IF 0.8 4区数学 Q3 Mathematics

Sequential Analysis-Design Methods and Applications

Pub Date : 2019-10-02 DOI: 10.1080/07474946.2019.1686937

N. Mukhopadhyay, Soumik Banerjee

Abstract We have designed a sequential minimum risk point estimation (MRPE) strategy for the unknown mean of a normal population having its variance unknown too. This is developed under a Linex loss plus linear cost of sampling. A number of important asymptotic first-order and asymptotic second-order properties' characteristics have been developed and proved thoroughly. Extensive sets of simulations tend to validate nearly all of these asymptotic properties for small to medium to large optimal fixed sample sizes.

摘要针对方差未知的正态群体的未知均值，我们设计了一种序列最小风险点估计（MRPE）策略。这是在Linex损耗加上线性采样成本的情况下开发的。已经发展并充分证明了许多重要的渐近一阶和渐近二阶性质的性质。大量的模拟往往会验证从小到中到大的最优固定样本量的几乎所有这些渐近性质。

引用次数: 3

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