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.

On Sequential Inference

Abstract: The idea of sequential inference is probably as old as that of induction itself. All traditional accounts of induction by simple enumeration say roughly this : elements of a class A are examined, one by one, for a property B; the process is continued until either (1) an element of A turns out to be not-B (in which case the hypothesis ‘all A are B’ is rejected), or (2) the inference maker is satisfied that he has accumulated enough evidence to accept the hypothesis ‘all A are B’. In spite of its crude form (no criterion of sufficient evidence is provided), the above procedure has certain properties characteristic of sequential inference. The accumulation of evidence on which the conclusion is to be based proceeds in consecutive steps ; their number is not determined in advance.

Obstructive distributions in a sequential rank-order test based on lehmann alternatives

Abstract: Publisher Summary This chapter discusses obstructive distributions in a sequential rank-order test based on Lehmann alternatives. Savage and Sethuraman considered the stopping time N of a sequential probability ratio test based on ranks for the following problem as per which if X and Y are real valued and independent random variables, possessing distribution functions F and G, respectively, the problem is to test sequentially the hypothesis G = F against the alternative G = F A for some given A ≠ 1. To this end, independent observations (X 1 , Y 1 ), (X 2 , Y 2 ) … on (X, Y) are taken and all information in the sample is discarded at each sampling stage except the ranks of the Ys among the Xs and Ys. This reduces the composite hypotheses to simple ones. The property of exponential boundedness of N is a desirable one. In the contrary case, when N is not exponentially bounded under P, P is obstructive. Complete or partial results on exponential boundedness of N and obstructive distributions have been obtained in several other testing situations.

Online Classification in 3D Urban Datasets Based on Hierarchical Detection

Abstract: One of the most significant problems in the area of 3D range image processing is that of segmentation and classification from 3D laser range data, especially in real-time. In this work we introduce a novel multi-layer approach to the classification of 3D laser scan data. In particular, we build a hierarchical framework of online detection and identification procedures drawn from sequential analysis namely the CUSUM (Cumulative Sum) and SPRT (Sequential Probability Ratio Test), both of which are low complexity algorithms. Each layer of algorithms builds upon the decisions made at the previous stage thus providing a robust framework of online decision making. In our new framework we are not only able to classify in coarse classes such as vertical, horizontal and/or vegetation but to also identify objects characterized by more subtle or gradual changes such as curbs or steps. Moreover, our new multi-layer approach combines information across scan lines and results in more accurate decision making. We perform experiments in complex urban scenes and provide quantitative results.

Reliability sequential compliance method for a partially observable gear system subject to vibration monitoring

Abstract: Assumptions accompanying exponential failure models are often not met in the standard sequential probability ratio test (SPRT) of many products. However, for most of the mechanical products, Weibull distribution conforms to their life distributions better compared to other techniques. The SPRT method for Weibull life distribution is derived in this paper, which enables the implementation of reliability compliance tests for gearboxes. Using historical failure data and condition monitoring data, a life prediction model based on hidden Markov model (HMM) is established to describe the deterioration process of gearboxes, then the predicted remaining useful life (RUL) is transformed into failure data that is used in SPRT for further analysis, which can significantly save on testing time and reduce costs. Explicit expression for the distribution of RUL is derived in terms of the posterior probability that the system is in the unhealthy state. The predicted and actual values of the residual life are compared, and the average relative error is 3.90 %, which verifies the validity of the proposed residual life prediction approach. A comparison with other life prediction and SPRT methods is given to elucidate the efficacy of the proposed approach.

A two-sample sequential test with one sample-size fixed.

Abstract: : When two populations must be sampled at different times, one cannot test for shift using the standard sequential probability ratio test based on paired observations. However, it is still meaningful to obtain the later sample sequentially. A test for shift with one sample-size fixed and the other sample-size random is proposed, some of its properties are developed under normal theory assumptions, and a comparison is made with the completely fixed sample-size procedure. (Author)