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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: It is possible to obtain any positive value for the Wald test statistic, by rewriting the null hypothesis being tested in an algebraically equivalent form as discussed by the authors, and it is also possible to derive a positive result for any positive test statistic.
Abstract: It is possible to obtain any positive value for the Wald test statistic, by rewriting the null hypothesis being tested In an algebraically equivalent form.
35 citations
TL;DR: In this article, the authors proposed stopping rules and decision rules for simultaneous testing of multiple hypotheses in sequential experiments, and derived asymptotically optimal procedures under Pitman alternative.
Abstract: Sequential procedures are developed for simultaneous testing of multiple hypotheses in sequential experiments. Proposed stopping rules and decision rules achieve strong control of both family-wise error rates I and II. The optimal procedure is sought that minimizes the expected sample size under these constraints. Bonferroni methods for multiple comparisons are extended to sequential setting and are shown to attain an approximately 50% reduction in the expected sample size compared with the earlier approaches. Asymptotically optimal procedures are derived under Pitman alternative.
35 citations
TL;DR: This model combined a model of noisy physical simulation with a decision making strategy called the sequential probability ratio test, or SPRT, and predicted that people should use more samples when it is harder to make an accurate prediction due to higher simulation uncertainty.
35 citations
TL;DR: In this article, a generalized sequential probability ratio test (GPRT) was proposed for the problem of testing one simple hypothesis against another, which differs from the Wald test only in that the same limits ($A, B$ in the usual notation) are not necessarily used at each stage of the sampling, but at the $i$th stage $A i and $B i are used, where these numbers are predetermined constants.
Abstract: For the problem of testing one simple hypothesis against another, of all tests whose probabilities of incorrectly accepting the first hypothesis and of incorrectly accepting the second hypothesis are bounded from above by given bounds, the familiar Wald sequential probability ratio test gives the smallest expectation of sample size under either hypothesis. In this paper, a "generalized sequential probability ratio test" is introduced which differs from the Wald test only in that the same limits ($A, B$ in the usual notation) are not necessarily used at each stage of the sampling, but at the $i$th stage $A_i$ and $B_i$ are used, where these numbers are predetermined constants. It is shown that for any given test $T$, there is a generalized sequential probability ratio test $G$ whose probabilities of incorrectly accepting either hypothesis are no larger than the corresponding probabilities for $T$, and such that the cumulative distribution function of the number of observations required to come to a decision when using $G$ is never below the corresponding distribution function when using $T$, under either hypothesis. We may then say that "$G$ is uniformly better than $T$."
35 citations
TL;DR: In this paper, a general problem of testing two simple hypotheses about the distribution of a discrete-time stochastic process is considered, and the main goal is to minimize an average sample number over all sequential tests whose error probabilities do not exceed some prescribed levels.
Abstract: A general problem of testing two simple hypotheses about the distribution of a discrete-time stochastic process is considered. The main goal is to minimize an average sample number over all sequential tests whose error probabilities do not exceed some prescribed levels. As a criterion of minimization, the average sample number under a third hypothesis is used (modified Kiefer–Weiss problem). For a class of sequential testing problems, the structure of optimal sequential tests is characterized. An application to the Kiefer–Weiss problem for discrete-time stochastic processes is proposed. As another application, the structure of Bayes sequential tests for two composite hypotheses, with a fixed cost per observation, is given. The results are also applied for finding optimal sequential tests for discrete-time Markov processes. In a particular case of testing two simple hypotheses about a location parameter of an autoregressive process of order 1, it is shown that the sequential probability ratio test...
35 citations