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.

Sequential probability ratio tests based on improper priors

Abstract: One way of handling composite hypotheses by SPRT's is to integrate out nuisance parameters under both the null and alternative hypotheses and then form an SPRT. If the prior is improper, Wald inequalities will not hold in general. We provide sufficient conditions and then verify that the usual sequential |t|-test satisfies these conditions but Wald's |t|-test does not satisfy these conditions and in fact cannot satisfy a strengthened form of these inequalities in general. Nonetheless, simulations show Wald's inequalities for A, B, corresponding to usual small α, β, will usually hold.

BERNOULLI SAMPLING PLANS WHICH APPROXIMATELY MINIMIZE THE MAXIMUM expected sample size subject to certAIN PROBABILITY REQUIREMENTS

Abstract: : The author, in his masters thesis, constructed a catalog of 442 Bernoulli sampling plans which approximately minimize the maximum expected sample size among all plans which guarantee certain O.C. probability requirements. Fifty-two of these plans (which would appear to be of greatest practical interest) are presented in this report. A.S.N. curve comparisons are made with plans based on the Wald sequential probability ratio test and the fixed sample size test which guarantee the same O.C. probability requirements.

Group Sequential Design for Randomized Phase III Trials under the Weibull Model

Abstract: In this article, a parametric sequential test is proposed under the Weibull model. The proposed test is asymptotically normal with an independent increment structure. The sample size for a fixed sample test is derived for the purpose of group sequential trial design. In addition, a multi-stage group sequential procedure is given under the Weibull model by applying the Brownian motion property of the test statistic and sequential conditional probability ratio test methodology.

Sample-size-optimal sequential testing

Abstract: Sequential sampling schemes have traditionally used ad hoc rules for sample size. The variable-sample-size sequential probability ratio test (VPRT), developed by Cressie and Morgan ( Proc. 4th Purdue Symp. on Decision Theory and Related Topics , IV Vol. 2, Springer, New York (1988), 107–118), generalizes the classical one-at-a-time and group-sequential procedures to an optimal procedure that maximizes the expected net gain of sampling, conditional on the accumulated observations on the stochastic process. In this paper, we apply the VPRT to the problem of sequential testing of a Gaussian mean.

Sequential Bayesian Detection: A Model-Based Approach

Abstract: Sequential detection is a methodology developed essentially by Wald [1] in the late 1940s providing an alternative to the classical batch methods evolving from the basic Neyman–Pearson theory of the 1930s [2, 3]. From the detection theoretical viewpoint, the risk (or error) associated with a decision typically decreases as the number of measurements increases. Sequential detection enables a decision to be made more rapidly (in most cases) employing fewer measurements while maintaining the same level of risk. Thus, the aspiration is to reduce the decision time while maintaining the risk for a fixed sample size. Its significance was truly brought to the forefront with the evolution of the digital computer and the fundamental idea of acquiring and processing data in a sequential manner. The seminal work of Middleton [2, 4, 5, 6, 7] as well as the development of sequential processing techniques [8, 9, 10, 11, 12, 13] during the 1960s provided the necessary foundation for the sequential processor/detector that is applied in a routine manner today [7, 8, 9, 10, 11, 13].