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.

A sequential procedure for simultaneous detection and state estimation of Markov signals

Abstract: The problem of joint detection and state estimation of a Markov signal when a variable number of noisy measurements can be taken is here considered. In particular, the signal-observation sequence {X i ;Z i } i∈N is a hidden Markov process (HMP) while, if the signal is absent, the measurement {Zi} i2∈N is an i.i.d. process. In this framework, two coupled detection and estimation procedures are introduced for the cases of discrete and continuous state space. Bounds on the performance of the proposed procedures in terms of the thresholds are derived, similar to the classical bounds for the sequential probability ratio test (SPRT). Moreover, it is shown that, under a set of rather mild conditions, the procedures end with probability one and the stopping time is almost surely minimized in the class of tests with the same or smaller error probabilities.

A bootstrapped sequential probability ratio test for signal processing applications

Abstract: A new algorithm is presented that combines the bootstrap and the generalized sequential probability ratio test. The latter replaces all unknown parameters with suitable estimates so that the test statistic is subject to uncertainty. The question of how to choose the decision thresholds for the generalized sequential probability ratio test such that it fulfills given constraints on the error probabilities is still open. We propose to address this problem not by adjusting the thresholds, but by bootstrapping the estimates of the unknown parameters and constructing confidence intervals for the test statistic. The stopping rule of the test is then defined in terms of this confidence interval instead of the test statistic itself. The proposed procedure is reliable and admits the beneficial properties of sequential tests in terms of the expected number of samples. It can hence be useful for applications where making observations is expensive or time critical, as is often the case in Internet-of-Things, data analytics or wireless communications.

Assessment of competency in clinical measurement: comparison of two forms of sequential test and sensitivity of test error rates to parameter choice.

Abstract: Objective To assess clinical measurement competency by two sequential test formulations [resetting sequential probability ratio test (R-SPRT) and learning curve cumulative summation (LC-CUSUM)]. Design Numerical simulation and retrospective observational study. Setting Obstetric ultrasound department. Participants Cohorts of 10 000 simulated trainees and 62 obstetric sonographers training in nuchal translucency (NT) measurement at the 11–14-week pregnancy scan with limited case availability. Intervention Application of LC-CUSUM and R-SPRT to clinical measurement training. Main Outcome Measures Proportions of real trainees achieving competency by LC-CUSUM and R-SPRT, proportions of simulated competent trainees not achieving competency (Type I error), proportions of simulated incompetent trainees achieving competency (Type II error), distribution of case number required to achieve competency (run length) and frequency of resets. Results For simulated cohorts, significant differences in run-length distribution and true test error rates were found between the R-SPRT and LC-CUSUM tests with equivalent parameters. Increasing the cases available to each trainee reduced the Type I error rate but increased the Type II error rate for both sequential tests for all choices of unacceptable failure rate. Discontinuities in the proportion of trainees expected to be test competent were found at critical values of unacceptable failure rate. Conclusions With equivalent parameters, the R-SPRT and LC-CUSUM formulations of sequential tests produced different outcomes, demonstrating that the choice of test method, as well as the choice of parameters, is important in designing a training scheme. The R-SPRT detects incompetence as well as competence and may indicate need for further training. Simulations are valuable in estimating the proportions of trainees expected to be assessed as competent.

An estimation method for the excess over the bocndaries in the sprt and its applications

Abstract: Since Wald developed the sequential probability ratio test, many studies have been done to approximate the characteristics of the test. One of the major efforts among them is to approximate the excess over the boundaries used in the test. In this paper the excess is approximated as a simple function of the parameter to be tested by using the condition of the test statistic immediately before the stopping time in normal and exponential cases. The use of the estimated excess shows good performances in estimating the operating characteristic function, the average sample number, and the probability mass function of the sarnple number. It also make it possible to determine the boundary values which can give the error probabilities close to the desired ones.