Topic
Sequential probability ratio test
About: Sequential probability ratio test is a research topic. Over the lifetime, 1248 publications have been published within this topic receiving 22355 citations.
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01 Jan 2003
TL;DR: Empirical evidence is presented on the robustness of the Sequential Probability Ratio Test (SPRT) and it was found that SPRT is robust in analyzing data with a small degree of serial-correlation and a quantifiable “false alarm robustness threshold“ was determined.
Abstract: In this paper, empirical evidence is presented on the robustness of the Sequential Probability Ratio Test (SPRT). The test utilizes user-specified false and missed alarm probabilities and detects the statistical changes in process signals at the earliest possible time. Earlier research has shown that, even when the analyzed signal distribution is not Gaussian, but a normal distribution is used in the theoretical analysis, SPRT appears to be robust. However, the user-specified false alarm probability may not be met when the analyzed signals contain serial-correlation. The Stochastic Parameter Simulation System has been used to obtain signals with various degrees of serialcorrelation. These signals were analyzed by SPRT and it was demonstrated that the number of SPRT false alarms increases as the degree of serial-correlation increases. It was also found that SPRT is robust in analyzing data with a small degree of serial-correlation and a quantifiable “false alarm robustness threshold“ was determined. Although this conclusion is based on the analysis of a relatively small number of observations, we believe that it is widely applicable and may have a powerful impact on signal monitoring and validation techniques that use SPRT as a fault detection algorithm.
26 Jun 2022
TL;DR: In this paper , a novel formulation based on sequential hypothesis testing is provided, and an algorithm for best arm identification is proposed that, in spirit, follows the structure of the canonical sequential probability ratio test (SPRT).
Abstract: This paper investigates the problem of best arm identification (BAI) in stochastic multi-armed bandits in the fixed confidence setting. A novel formulation based on sequential hypothesis testing is provided, and an algorithm for BAI is proposed that, in spirit, follows the structure of the canonical sequential probability ratio test (SPRT). The algorithm has three features: (1) its sample complexity is asymptotically optimal, (2) it is guaranteed to be δ-PAC, and (3) it addresses the computational challenge of the state-of-the-art approaches. Specifically, the existing approaches rely on Thompson sampling for dynamically identifying the best arm and a challenger. This paper shows that identifying the challenger can be computationally expensive and demonstrates that the SPRT-based approach addresses that computational weakness.
08 Mar 2023
TL;DR: In this paper , an optimal sequential test of sum of logarithmic likelihood ratio (SLR) with the observation-adjusted control limits (CUSUM-OAL) was proposed.
Abstract: In this paper, we not only propose an new optimal sequential test of sum of logarithmic likelihood ratio (SLR) but also present the CUSUM sequential test (control chart, stopping time) with the observation-adjusted control limits (CUSUM-OAL) for monitoring quickly and adaptively the change in distribution of a sequential observations. Two limiting relationships between the optimal test and a series of the CUSUM-OAL tests are established. Moreover, we give the estimation of the in-control and the out-of-control average run lengths (ARLs) of the CUSUM-OAL test. The theoretical results are illustrated by numerical simulations in detecting mean shifts of the observations sequence.
01 Mar 2017
TL;DR: It is shown that, under certain regularity conditions on the data distribution and network topology, this distributed sequential test procedure yields the order-2 asymptotically optimal performance at all sensors.
Abstract: This work considers the sequential hypothesis testing problem in the fully distributed sensor network. In specific, each sensor can observe samples over time, exchange information with adjacent sensors, and perform testing based on its own locally available decision statistic. Under such setting, we study the sequential probability ratio test based on the statistic that is obtained by running consensus algorithm. It is shown that, under certain regularity conditions on the data distribution and network topology, this distributed sequential test procedure yields the order-2 asymptotically optimal performance at all sensors.
Journal Article•
TL;DR: In this article, the authors developed a sequential probability ratio test (SPRT) for the scale parameter of Nakagami distribution and the robustness of scale parameter is studied when the shape parameter has undergone a change.
Abstract: In the present study, Sequential Probability Ratio Test (SPRT) is developed for the scale parameter of Nakagami Distribution and the robustness of scale parameter is studied when the shape parameter has undergone a change, for testing the hypothesis regarding the parameter of Nakagami Distribution. The expression for the Operating Characteristic (OC) and Average Sample Number (ASN) functions are derived and the results are presented through Graphs and Tables.