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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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29 Oct 2012
TL;DR: In this article, the authors proposed a filter bank consisting of an ordinary current-state extended Kalman filter and two similar but constrained filters: one is constrained by a null hypothesis that the miss distance between two conjuncting spacecraft is inside their combined hard body radius at the predicted time of closest approach, and one was constrained by an alternative complementary hypothesis.
Abstract: We propose a filter bank consisting of an ordinary current-state extended Kalman filter, and two similar but constrained filters: one is constrained by a null hypothesis that the miss distance between two conjuncting spacecraft is inside their combined hard body radius at the predicted time of closest approach, and one is constrained by an alternative complementary hypothesis. The unconstrained filter is the basis of an initial screening for close approaches of interest. Once the initial screening detects a possibly risky conjunction, the unconstrained filter also governs measurement editing for all three filters, and predicts the time of closest approach. The constrained filters operate only when conjunctions of interest occur. The computed likelihoods of the innovations of the two constrained filters form a ratio for a Wald sequential probability ratio test. The Wald test guides risk mitigation maneuver decisions based on explicit false alarm and missed detection criteria. Since only current-state Kalman filtering is required to compute the innovations for the likelihood ratio, the present approach does not require the mapping of probability density forward to the time of closest approach. Instead, the hard-body constraint manifold is mapped to the filter update time by applying a sigma-point transformation to a projection function. Although many projectors are available, we choose one based on Lambert-style differential correction of the current-state velocity. We have tested our method using a scenario based on the Magnetospheric Multi-Scale mission, scheduled for launch in late 2014. This mission involves formation flight in highly elliptical orbits of four spinning spacecraft equipped with antennas extending 120 meters tip-to-tip. Eccentricities range from 0.82 to 0.91, and close approaches generally occur in the vicinity of perigee, where rapid changes in geometry may occur. Testing the method using two 12,000-case Monte Carlo simulations, we found the method achieved a missed detection rate of 0.1%, and a false alarm rate of 2%.

5 citations

01 Jan 2010
TL;DR: This paper introduces a novel numerical representation of the performance of decentralized decision making in a population of individuals each implementing the sequential probability ratio test and describes the tradeoff between accuracy and decision time as a function of the population size.

5 citations

Journal ArticleDOI
TL;DR: A new diagnostic theory for the design of automated medical questioning equipment which tabulates the answers to questions into a form easily understood by physicians, which enumerates data on doubtful diseases and which indicates pertinent medical examinations may come to the aid of patients and physicians is presented.
Abstract: A medical interview is a very important part of medical treatment since it is conducted when a patient is first admitted to a hospital and treatment is decided afterwards. However, these interviews are not always carried out in sufficient detail because physicians have very heavy work-loads. The development of automated medical questioning equipment which tabulates the answers to questions into a form easily understood by physicians, which enumerates data on doubtful diseases and which indicates pertinent medical examinations may come to the aid of patients and physicians. This paper presents a new diagnostic theory for the design of automated medical questioning equipment. Diagnostic theories can be classified into batch and sequential theories; the authors have investigated the sequential one, because decisions are made using minimal data. The techniques supporting this theory are multi-class recognition systems based on independently designed dual-class recognition systems and Wald's Sequential Probability Ratio Test. To discuss the properties inherent in the present theory, classification of three pattern classes was made. These were normal, hypertension and myocardial infarction classes of patients. The mean error probability of classification was found to be 3.08%.

5 citations

Proceedings ArticleDOI
01 Jul 2015
TL;DR: The theoretical validity of 2-SPRT is proved for the problem of testing hypotheses with multivariate normal densities and a method of forced independence and identical distribution to optimally map the non-i.i.d. likelihood ratio sequence is presented.
Abstract: Double sequential probability ratio test (2-SPRT), as an extended version of SPRT to cope with the no-upper-bound problem, is extended to the multiple-model hypothesis testing (MMHT) approach, called 2-MMSPRT, for detecting unknown events that may have multiple prior distributions. Not only does it address the mis-specified problem of the SPRT based MMHT method (MMSPRT), but it also can be expected to provide most efficient detection in the sense of minimizing the maximum expected sample size subject to error probability constraints. Specifically, we proved the theoretical validity of 2-SPRT for the problem of testing hypotheses with multivariate normal densities. Moreover, we present a method of forced independence and identical distribution (i.i.d.) to optimally map the non-i.i.d. likelihood ratio sequence to an i.i.d. one, by which we solve the problem of SPRT and 2-SPRT for dynamic systems with a non-identical distribution. Finally, 2-MMSPRT's asymptotic efficiency is also verified. Performance of 2-MMSPRT is evaluated for model-set selection problems in several scenarios. Simulation results demonstrate the asymptotic effectiveness of the proposed 2-MMSPRT compared with the MMSPRT.

5 citations

01 Jan 1985
TL;DR: In this article, the behavior of Wald's test when applied to hypothesis testing in exponential families is studied and conditions under which the test statistic decreases to zero as the parameter estimate moves away from the null value are derived.
Abstract: Summary Hauck & Donner (1977) showed that Wald's test (the maximum likelihood test statistic) behaves in an aberrant manner when applied to hypotheses about a single parameter in a binomial logit model. In particular they have shown that the test statistic decreases to zero as the parameter estimate moves away from the null value. In the present work the behaviour of Wald's test when applied to hypothesis testing in exponential families is studied. The investigation is mainly restricted to the one-sample problem for one-parameter exponential families. Conditions under which Wald's test is well behaved and conditions under which Wald's test may be misleading are derived. It is shown that the problem occurs in connection with certain parameterizations of discrete probability distributions and also, in the continuous case, if the upper tail of the distribution function is approximately proportional to t-e-e' for some positive 0. Finally, the use of Wald's test in the analysis of generalized linear models is discussed.

5 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20236
202223
202129
202023
201929
201832