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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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TL;DR: In this paper, a sequential Gaussian shift-in-mean hypothesis testing in a distributed multi-agent network is studied, where the agents update their decision statistics by simultaneously processing latest observations (innovations) sensed sequentially over time and information obtained from neighboring agents.
Abstract: This paper studies the problem of sequential Gaussian shift-in-mean hypothesis testing in a distributed multi-agent network. A sequential probability ratio test (SPRT) type algorithm in a distributed framework of the consensus+innovations form is proposed, in which the agents update their decision statistics by simultaneously processing latest observations (innovations) sensed sequentially over time and information obtained from neighboring agents (consensus). For each pre-specified set of type I and type II error probabilities, local decision parameters are derived which ensure that the algorithm achieves the desired error performance and terminates in finite time almost surely (a.s.) at each network agent. Large deviation exponents for the tail probabilities of the agent stopping time distributions are obtained and it is shown that asymptotically (in the number of agents or in the high signal-to-noise-ratio regime) these exponents associated with the distributed algorithm approach that of the optimal centralized detector. The expected stopping time for the proposed algorithm at each network agent is evaluated and is benchmarked with respect to the optimal centralized algorithm. The efficiency of the proposed algorithm in the sense of the expected stopping times is characterized in terms of network connectivity. Finally, simulation studies are presented which illustrate and verify the analytical findings.
33 citations
33 citations
TL;DR: It is shown that a class of SPRT boundaries is minimax with respect to resampling risk and recommended a truncated version of boundaries in that class by comparing their resamplings risk (RR) to the RR of fixed boundaries with the same maximum resample size.
Abstract: When designing programs or software for the implementation of Monte Carlo (MC) hypothesis tests, we can save computation time by using sequential stopping boundaries. Such boundaries imply stopping resampling after relatively few replications if the early replications indicate a very large or a very small p value. We study a truncated sequential probability ratio test (SPRT) boundary and provide a tractable algorithm to implement it. We review two properties desired of any MC p value, the validity of the p value and a small resampling risk, where resampling risk is the probability that the accept/reject decision will be different than the decision from complete enumeration. We show how the algorithm can be used to calculate a valid p value and confidence intervals for any truncated SPRT boundary. We show that a class of SPRT boundaries is minimax with respect to resampling risk and recommend a truncated version of boundaries in that class by comparing their resampling risk (RR) to the RR of fixed boundari...
33 citations
TL;DR: It is shown that this sequential test is asymptotically optimal in the sense that it achieves asymPTotically the shortest expected sample size as the maximal type I and type II error probabilities tend to zero.
Abstract: In this paper, we consider the problem of testing two separate families of hypotheses via a generalization of the sequential probability ratio test. In particular, the generalized likelihood ratio statistic is considered and the stopping rule is the first boundary crossing of the generalized likelihood ratio statistic. We show that this sequential test is asymptotically optimal in the sense that it achieves asymptotically the shortest expected sample size as the maximal type I and type II error probabilities tend to zero.
33 citations
01 May 2007
TL;DR: This paper revisits the problem of detecting greedy behavior in the IEEE 802.11 MAC protocol by evaluating the performance of two previously proposed schemes: DOMINO and the sequential probability ratio test (SPRT), and derives a new analytical formulation of the SPRT that takes into account the discrete nature of the problem.
Abstract: This paper revisits the problem of detecting greedy behavior in the IEEE 802.11 MAC protocol by evaluating the performance of two previously proposed schemes: DOMINO and the sequential probability ratio test (SPRT). The evaluation is carried out in four steps. We first derive a new analytical formulation of the SPRT that takes into account the discrete nature of the problem. Then we develop a new tractable analytical model for DOMINO. As a third step, we evaluate the theoretical performance of SPRT and DOMINO with newly introduced metrics that take into account the repeated nature of the tests. This theoretical comparison provides two major insights into the problem: it confirms the optimality of SPRT and motivates us to define yet another test, a nonparametric CUSUM statistic that shares the same intuition as DOMINO but gives better performance. We finalize the paper with experimental results, confirming our theoretical analysis and validating the introduction of the new nonparametric CUSUM statistic.
33 citations