An information-theoretic approach to incorporating prior information in binomial sampling

Dyer, Danny; Chiou, Paul

doi:10.1080/03610928408828813

Cited by 27 publications

(11 citation statements)

References 12 publications

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“…Table 5.1 illustrates that system reliability for a process with a random M , with E(M ) = m, is at least as large as the system reliability in a known number of tasks, m. It also shows that these reliabilities are again very similar for the Poisson and the deterministic cases. Comparing Table 5.1 with Table 2 Table 5.1: r(1, 2|m = 5, (20, 0)) and r(1, 2|M ∼ Po (5), (20,0)) for varying α, β.…”

Section: Example 521mentioning

confidence: 99%

“…In addition, the parameters of Beta distributions can easily be interpreted, an important advantage when we consider the influence of the prior distribution on the required test numbers later in this thesis. Dyer and Chiou [20] found in their research that the Beta family is the most suitable, comparing to other families of priors, when prior information about the system is not available. Colombo and Constantini [11,12] support the Beta distribution as Bayesian prior with Binomial sampling.…”

Section: Learning From Testsmentioning

confidence: 99%

“…For β = 0 and α = 1, (5.4) yields 19) the proof of which is given in Appendix A.2. Hence, the minimal number of zerofailure tests, n, required to demonstrate a level of reliability p, can be obtained 20) which leads to…”

Section: Reliability Demonstration For a Single Taskmentioning

confidence: 99%

“…Moreover, although we do not have an analytic proof of the following statement, the study of many examples suggests that the difference between these probabilities for the deterministic and the Poisson cases is very small. (5) Table 2.1: P (0|m = 5, (20, 0)) and P (F F P |M ∼ Po (5), (20,0)) for varying α, β.…”

Section: The Poisson Casementioning

confidence: 99%

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Probabilistic Assessment Study of Channels Downstream Slopes Erosion in the Maritime Environment

Khalifa

Ganainy

Nasr

2009

Journal of Coastal Research

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We study required numbers of tasks to be tested for a technical system, including systems with built-in redundancy, in order to demonstrate its reliability with regard to its use in a process after testing, where the system has to function for different types of tasks, which we assume to be independent. We consider optimal numbers of tests as required for Bayesian reliability demonstration in terms of failure-free periods, which is suitable in case of catastrophic failures, and in terms of the expected number of failures in a process after testing. We explicitly assume that testing reveals zero failures. For the process after testing, we consider both deterministic and random numbers of tasks. We also consider optimal numbers of tasks to be tested when aiming at minimal total expected costs, including costs of testing and of failures in the process after testing. Cost and time constraints on testing are also included in the analysis. We consider such reliability demonstration for a single type of task, as well as for multiple types of tasks to be performed by one system. We also consider optimal Bayesian reliability demonstration testing in combination with flexibility in the system redundancy, where more components can be installed to reduce test effort. For systems with redundancy, we restrict attention to systems with exchangeable components, with testing only at the component level.We use the Bayesian approach with the Binomial model and Beta prior distributions for the failure probabilities. We discuss the influence of choice of prior distribution on the required zero-failure test numbers, where these inferences are very sensitive to the choice of prior distribution, which requires careful attention to the interpretation of non-informativeness of priors. DeclarationThe work in this thesis is based on research carried out at the Statistics and Probability Group, Department of Mathematical Sciences, University of Durham, England.No part of this thesis has been submitted elsewhere for any other degree or qualification and it is all my own work unless referenced to the contrary in the text.

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Section: Example 521mentioning

confidence: 99%

Section: Learning From Testsmentioning

confidence: 99%

Section: Reliability Demonstration For a Single Taskmentioning

confidence: 99%

Section: The Poisson Casementioning

confidence: 99%

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Probabilistic Assessment Study of Channels Downstream Slopes Erosion in the Maritime Environment

Khalifa

Ganainy

Nasr

2009

Journal of Coastal Research

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“…T o overcome these weaknesses, procedures to create noninformative priors have been suggested by a number of authors (Jeffreys 1961;Lindley 1956Lindley , 1961Hartigan 1964;Novick and Hall 1965;Box and Tiao 1973;Jaynes 1968;Zellner 1971). As a n alternative, a method presented by Dyer and Chiou (1984) was based on an information-theoretic approach and developed for the binomial sampling model. This approach can be used when little or no information is available or when a substantial amount of information is available.…”

Section: Introductionmentioning

confidence: 99%

On the choice of the prior distribution in hypergeometric sampling

Dyer

Pierce

1993

Communications in Statistics - Theory and Methods

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Information in a statistical procedure arising from sources other than sampling is called prior information, and its incorporation into the procedure forms the basis of the Bayesian approach to statistics. Under hypergeometric sampling, methodology is developed which quantifies the amount of information provided by the sample d a t a relative to that provided by the prior distribution and allows for a ranking of prior distributions with respect to conservativeness, where conservatism refers t o restraint of extraneous information embedded in any prior distribution. The most conservative prior distribution from a specified class (each member of which carries the available prior information) is that prior distribution within the class over which the likelihood function has the greatest average domination. Four different families of prior distributions are developed by considering a Bayesian approach to the formation of lots. The most conservative prior distribution from each of the four families of prior distributions is determined and compared for the situation when no prior information is available. T h e results of the comparison advocate the use of the Polya (beta-binomial) prior distribution in hypergeometric sampling.

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