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 note on efficient performance evaluation of the Cumulative Sum chart and the Sequential Probability Ratio Test

Abstract: We establish a simple connection between certain in-control characteristics of the Cumulative Sum CUSUM Run Length and their out-of-control counterparts. The connection is in the form of paired integral renewal equations. The derivation exploits Wald's likelihood ratio identity and the well-known fact that the CUSUM chart is equivalent to repetitive application of Wald's Sequential Probability Ratio Test SPRT. The characteristics considered include the entire Run Length distribution and all of the corresponding moments, starting from the zero-state average run length. A particular practical benefit of our result is that it enables the in-control and out-of-control characteristics of the CUSUM Run Length to be computed concurrently. Moreover, owing to the equivalence of the CUSUM chart to a sequence of SPRTs, the Average Sample Number and Operating Characteristic functions of an SPRT under the null and under the alternative can all be computed simultaneously as well. This would double up the efficiency of any numerical method that one may choose to devise to carry out the actual computations. Copyright © 2016 John Wiley & Sons, Ltd.

Classical Nonparametric Hypothesis Tests with Applications in Social Good

Abstract: Author(s): Ottoboni, Kellie | Advisor(s): Stark, Philip B | Abstract: Hypothesis testing has come under fire in the past decade as misuses have become increas- ingly visible. It is common to use tests whose assumptions don’t reflect how the data were collected, and editorial policies of many journals reward “p-hacking” by setting the arbitrary threshold of 0.05 to determine whether a result merits publication. In fact, properly designed hypothesis tests are an invaluable tool for inference and decision-making. Classical nonparametric tests, once reserved for problems that could be worked out with pencil and paper or approximated asymptotically, can now be applied to complex datasets with the help of modern computing power. This dissertation tailors some nonparametric tests to modern applications for social good.Permutation tests are a class of hypothesis tests for data that involve random (or plausibly random) assignment. The parametric assumptions for common tests, like the t-test and linear regression, may not hold for randomized experiments; in contrast, the assumptions of permutation tests are implied by the experimental design. But off-the-shelf permutation tests are not a panacea: tests must be tailored to fit the experimental design, and there are subtle numerical issues with implementing the tests in software. We construct permutation tests and software to address particular questions in randomized and natural experiments, including identifying what, if anything, student evaluations of teaching measure, and whether voting machines malfunctioned in Georgia’s November 2018 election.Risk-limiting post-election audits (RLAs) have existed for a decade, but have not been adopted widely, in part due to logistical hurdles. This thesis uses classical nonparametric techniques, including Fisher’s combination method and Wald’s sequential probability ratio test, to build new RLA methods that accommodate the idiosyncratic logistics of statewide elections. A new, more flexible method for using stratified samples in RLAs makes it easier and more efficient to audit elections conducted on heterogeneous voting equipment. This thesis also develops an RLA method based on Bernoulli sampling, which allows ballots to be audited “in parallel” across precincts on Election Day. The RLA method for stratified samples of ballots was piloted in Michigan to study its performance in the face of real-world constraints.

Research of small pipeline leak detection applied SPRT algorithm

Abstract: Sequential probability ratio test(SPRT) is put forward to detect and locate small leakage.Unitary new information sequence generated after Kalman Filter processing can be used to input sequence of SPRT to satisfy the requests.Methods of judging and locating leakage are analysed.At last,Kalman Filter and SPRT algorithms are realized with virtual instrument software,LabVIEW.The programming modules can be directly used in the existing pipeline leakage real-time detecting system.The experiments show that the design of rational and effective procedures for leakage of less than 3% of the small leak is also very effective and controls the positioning accuracy within 2.5%.

Efficiency in sequential testing: Comparing the sequential probability ratio test and the sequential Bayes factor test

Abstract: In a sequential hypothesis test, the analyst checks at multiple steps during data collection whether sufficient evidence has accrued to make a decision about the tested hypotheses. As soon as sufficient information has been obtained, data collection is terminated. Here, we compare two sequential hypothesis testing procedures that have recently been proposed for use in psychological research: Sequential Probability Ratio Test (SPRT; Psychological Methods, 25(2), 206-226, 2020) and the Sequential Bayes Factor Test (SBFT; Psychological Methods, 22(2), 322-339, 2017). We show that although the two methods have different philosophical roots, they share many similarities and can even be mathematically regarded as two instances of an overarching hypothesis testing framework. We demonstrate that the two methods use the same mechanisms for evidence monitoring and error control, and that differences in efficiency between the methods depend on the exact specification of the statistical models involved, as well as on the population truth. Our simulations indicate that when deciding on a sequential design within a unified sequential testing framework, researchers need to balance the needs of test efficiency, robustness against model misspecification, and appropriate uncertainty quantification. We provide guidance for navigating these design decisions based on individual preferences and simulation-based design analyses.

An Information Theoretic Analysis of Sequential Decision-Making

Abstract: We provide a novel analysis of Wald's sequential probability ratio test based on information theoretic measures for symmetric thresholds, symmetric noise, and equally likely hypotheses under the assumption that the test exactly terminates at one of the thresholds. This test is optimal in the sense that it yields the minimum mean decision time. To analyze the decision-making process we consider information densities, which represent the stochastic information content of the observations yielding a stochastic termination time of the test. Based on this, we show that the conditional probability to decide for hypothesis $\mathcal{H}_1$ (or the counter-hypothesis $\mathcal{H}_0$) given that the test terminates at time instant $k$ is independent of time $k$. An analogous property has been found for a continuous-time first passage problem with two absorbing boundaries in the contexts of non-equilibrium statistical physics and communication theory. Moreover, we study the evolution of the mutual information between the binary variable to be tested and the output of the Wald test. Notably, we show that the decision time of the Wald test contains no information on which hypothesis is true beyond the decision outcome.