Multihypothesis sequential probability ratio tests - Part I: Asymptotic optimality

  title={Multihypothesis sequential probability ratio tests - Part I: Asymptotic optimality},
  author={Vladimir P. Dragalin and Alexander G. Tartakovsky and Venugopal V. Veeravalli},
  journal={IEEE Trans. Inf. Theory},
The problem of sequential testing of multiple hypotheses is considered, and two candidate sequential test procedures are studied. Both tests are multihypothesis versions of the binary sequential probability ratio test (SPRT), and are referred to as MSPRTs. The first test is motivated by Bayesian optimality arguments, while the second corresponds to a generalized likelihood ratio test. It is shown that both MSPRTs are asymptotically optimal relative not only to the expected sample size but also… 
Multihypothesis sequential probability ratio tests - Part II: Accurate asymptotic expansions for the expected sample size
For pt. I see ibid. vol.45, p.2448-61, 1999. We proved in pt.I that two specific constructions of multihypothesis sequential tests, which we refer to as multihypothesis sequential probability ratio
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Abstract This article considers the problem of sequential testing of two composite hypotheses. Each of the hypotheses is described by a probability density function depending on a parameter. The
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The problem of testing two simple hypotheses about unknown local characteristics of several independent Brownian motions and compound Poisson processes is considered by considering the problem in its multisource setting and a Bayes optimal rule is identified by solving an optimal stopping problem for the likelihood-ratio process.
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The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second,
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We propose the weighted expected sample size (WESS) to evaluate the overall performance on the indifference-zones for three composite hypotheses’ testing problem. Based on minimizing the WESS to
Operating Characteristic and Average Sample Number of Binary and Multi-Hypothesis Sequential Probability Ratio Test
Based on the governing equations for OC and ASN of the SPRT developed in the previous work, a solution for the general case is proposed that relies on approximating the original test by truncation, that is, truncating the test at some finite time K.
Parametrized design of the generalized sequential probability ratio test
  • Naeem Akl, A. Tewfik
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    2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
  • 2017
This paper forms the binary sequential hypothesis testing as an optimization problem and proposes a generalization of the greedy approach that allows the designer to trade off complexity for closeness of the thresholds to their optimal values.


Asymptotic Optimality of Certain Multihypothesis Sequential Tests: Non‐i.i.d. Case
This paper shows that two specific constructions of sequential tests asymptotically minimize not only the expected time of observation but also any positive moment of the stopping time distribution under fairly general conditions for a finite number of simple hypotheses.
Multihypothesis sequential probability ratio tests - Part II: Accurate asymptotic expansions for the expected sample size
For pt. I see ibid. vol.45, p.2448-61, 1999. We proved in pt.I that two specific constructions of multihypothesis sequential tests, which we refer to as multihypothesis sequential probability ratio
A sequential procedure for multihypothesis testing
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It is well known that Wald's SPRT for testing simple hypotheses based on i.i.d. observations minimizes the expected sample size both under the null and under the alternative hypotheses among all
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Bounds on error probabilities and asymptotic expressions for the stopping time and error probabilities are given and a key result of this correspondence is a proof that the generalized MSPRT is asymptonically efficient.
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Combinations of one-sided sequential probability ratio tests (SPRT's) are shown to be "nearly optimal" for problems involving a finite number of possible underlying distributions. Subject to error
Sequential Analysis and Optimal Design
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A minimax regret test is proposed for deciding whether one of N populations has slipped to the right of the rest, under the null hypothesis that all populations are identical. The problem is
Sequential Analysis: Tests and Confidence Intervals
I Introduction and Examples.- II The Sequential Probability Ratio Test.- III Brownian Approximations and Truncated Tests.- IV Tests with Curved Stopping Boundaries.- V Examples of Repeated