Sequential Decision Problem: Algebraic Structure Theory of Sequential Machines . J. Hartmanis and R. E. Stearns. Prentice-Hall, Englewood Cliffs, N.J., 1966. 221 pp., illus. $12.

Science ◽  
1967 ◽  
Vol 156 (3774) ◽  
pp. 498-499
Author(s):  
Michael J. Flynn
Keyword(s):  
Algebraic Structure ◽  
Decision Problem ◽  
Structure Theory ◽  
Sequential Decision ◽  
Sequential Machines

Algebraic Structure Theory of Sequential Machines

1968 ◽  
Vol 22 (101) ◽  
pp. 235
Author(s):  
Eric G. Wagner ◽  
J. Hartmanis ◽  
R. E. Stearns
Keyword(s):  
Algebraic Structure ◽  
Structure Theory ◽  
Sequential Machines

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.

scholarly journals Trapping the Ultimate Success

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 158
Author(s):  
Alexander Gnedin ◽  
Zakaria Derbazi
Keyword(s):  
Decision Problem ◽  
Bernoulli Trials ◽  
Sequential Decision ◽  
Choice Problem ◽  
Best Choice Problem

We introduce a betting game where the gambler aims to guess the last success epoch in a series of inhomogeneous Bernoulli trials paced randomly in time. At a given stage, the gambler may bet on either the event that no further successes occur, or the event that exactly one success is yet to occur, or may choose any proper range of future times (a trap). When a trap is chosen, the gambler wins if the last success epoch is the only one that falls in the trap. The game is closely related to the sequential decision problem of maximising the probability of stopping on the last success. We use this connection to analyse the best-choice problem with random arrivals generated by a Pólya-Lundberg process.

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