SimSPRT-II: Monte Carlo Simulation of Sequential Probability Ratio Test Algorithms for Optimal Prognostic Performance

2016 ◽  
Author(s):  
Tahereh Masoumi ◽  
Kenny C. Gross
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Sequential Probability Ratio Test ◽  
Ratio Test ◽  
Prognostic Performance ◽  
Probability Ratio ◽  
Sequential Probability

Accuracy of sequential sampling plans based on Wald's sequential probability ratio test

1983 ◽  
Vol 13 (6) ◽  
pp. 1197-1203 ◽  
Author(s):  
Gary W. Fowler
Keyword(s):  
Monte Carlo ◽  
Sequential Sampling ◽  
Sequential Probability Ratio Test ◽  
Ratio Test ◽  
Type I ◽  
Sample Number ◽  
Sampling Plans ◽  
Probability Ratio ◽  
Sequential Probability ◽  
Relative Errors

Monte Carlo operating characteristic (OC) and average sample number (ASN) functions were compared with Wald's OC and ASN equations for sequential sampling plans based on Wald's sequential probability ratio test (SPRT) using the binomial, negative binomial, normal, and Poisson distributions. This comparison showed that the errors inherent in Wald's equations as a result of "overshooting" the decision boundaries of the SPRT can be large. Relative errors increased for the OC and ASN equations as the difference between the null (θ0)) and alternative (θ1) test parameter values increased. Relative errors also increased for the ASN equation as the probabilities of type I (α) and type II (β) errors increased. For discrete distributions, the relative errors also increased as θ0 increased with θ1/θ0 fixed. Wald's equations, in general, overestimate the true error probabilities and underestimate the true ASN. For the values of θ0, θ1, α, and β used in many sequential sampling plans in forestry, Wald's equations may not be adequate. For those cases where the errors in Wald's equations are important compared with the other errors associated with the sampling plan, two alternative Monte Carlo OC and ASN functions are proposed.

scholarly journals The VPRT: A Sequential Testing Procedure Dominating the SPRT

1993 ◽  
Vol 9 (3) ◽  
pp. 431-450 ◽  
Author(s):  
Noel Cressie ◽  
Peter B. Morgan
Keyword(s):  
Sample Size ◽  
Decision Problem ◽  
Sequential Analysis ◽  
Testing Procedure ◽  
Sequential Probability Ratio Test ◽  
Ratio Test ◽  
Sequential Decision ◽  
Probability Ratio ◽  
Sampling Cost ◽  
Sequential Probability

Under more general assumptions than those usually made in the sequential analysis literature, a variable-sample-size-sequential probability ratio test (VPRT) of two simple hypotheses is found that maximizes the expected net gain over all sequential decision procedures. In contrast, Wald and Wolfowitz [25] developed the sequential probability ratio test (SPRT) to minimize expected sample size, but their assumptions on the parameters of the decision problem were restrictive. In this article we show that the expected net-gain-maximizing VPRT also minimizes the expected (with respect to both data and prior) total sampling cost and that, under slightly more general conditions than those imposed by Wald and Wolfowitz, it reduces to the one-observation-at-a-time sequential probability ratio test (SPRT). The ways in which the size and power of the VPRT depend upon the parameters of the decision problem are also examined.

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