Letter to the Editor, Combining Probability Distributions from Experts in Risk Analysis

Publication Date Apr 30, 2000 by Kaplan S.

In their well-researched and almost unbelievably comprehensive paper, Clemen and Winkler (1) give a summary of my "Expert Information" method originally published in 1992. (2) From this summary, and from rereading the original paper, I recognize that in that paper I failed to adequately communicate my idea, probably because the idea at that time was newly formed in my mind.

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Beyond the Domain of Direct Observation: How to Specify a Probability Distribution that Represents the ‘State of Knowledge’ About Uncertain Inputs

Publication Date Feb 28, 1999 by Hoffman O., Kaplan S.

Uncertainty is inherent in all exposure and risk assessments in which mathematical models are used to extrapolate information beyond the domain of direct observation. Uncertainty exists because models are imperfect mimics of reality.

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An Improved Condensation Procedure in Discrete Probability Distribution Calculations

Publication Date Mar 31, 1987 by Kaplan S., Lin J.C.

A "vertical" condensation scheme for discrete probability distribution (DPD) calculations is presented as an alternative to the earlier "horizontal" scheme, an example of which was presented recently by Kurth and Cox. When applied to DPDs over a space of curves, the vertical condensation results in a "regularization" of the "spaghetti" of curves that results from combination operations on such DPDs.

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On the Use of Data and Judgment in Probabilistic Risk and Safety Analysis

Publication Date May 01, 1986 by Kaplan S.

This paper reviews the line of thought of a nuclear plant probabilistic risk analysis (PRA) identifying the points where data and judgment enter. At the "bottom" of the process, data and judgment are combined, using one and two stage Bayesian methods, to express what is known about the element of variables.

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On a Two-Stage Bayesian Procedure for Determining Failure Rates from Experiential Data

Publication Date Jan 31, 1983 by Kaplan S.

A process is described for analyzing failure data in which Bayes' theorem is used twice, firstly to develop a "prior" or "generic" probability distribution and secondly to specialize this distribution to the specific machine or system in question. The process is shown by examples to be workable in practice as well as simple and elegant in concept.

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On the Method of Discrete Probability Distributions in Risk and Reliability Calculations–Application to Seismic Risk Assessment

Publication Date Sep 30, 1981 by Kaplan S.

If the point of view is adopted that in calculations of real-world phenomena we almost invariably have significant uncertainty in the numerical values of our parameters, then, in these calculations, numerical quantities should be replaced by probability distributions and mathematical operations between these quantities should be replaced by analogous operations between probability distributions.

Sep 30, 1981

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Numerical Studies of the Partial Differential Equations Governing Nerve Impulse Conduction: The Effect of Lieberstein’s Inductance Term

Publication Date Aug 01, 1980 by Kennedy R.P., Cornell C.A., Campbell R.D., Kaplan S., Perla H.F.

The role of the inductance term in the equations for nerve impulse propagation is investigated by numerically solving these equations for various values of inductance. It is found that a full-fledged action potential develops for all values of inductance. The propagation velocity of the impulse is independent of inductance when the inductance is small. Larger values of inductance do affect the propagation velocity, but in no case is this velocity equal to that suggested by the linear wave operator portion of the governing equation.

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The Inverse Problem of Radioisotope Diagnosis; A Computational Method for Determining the Location and Size of Tumors

Publication Date Aug 01, 1969 by Kaplan S., McNabb A., Trujillo D., Siemsen J.K.

An idea is presented for an approach to the problem of finding lesions through interpretation of radioisotope scan data. The approach proposed includes an experimental measurement of the appropriate Green's function and some mathematical tricks for solving the resulting inverse problem. The tricks are illustrated by numerical examples. Pitfalls in the approach are pointed out and devices for overcoming them discussed.

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Canonical and Involutory Transformations of Variational Problems Involving Higher Derivatives

Publication Date Apr 01, 1968 by Kaplan S.

An exposition has been given of the notions of canonical and involutory transformation in the context of variational problems involving second derivatives of the argument function. As a specific illustration the variational problem representing a beam on nonlinear-elastic foundation is discussed.

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On the Use of Dual Variational Principles for the Estimation of Error in Approximate Solutions of Diffusion Problems

Publication Date May 01, 1967 by YaSinsky J.B., Kaplan S.

An exploration is made into a method for using reciprocal variational problems to develop figures of merit or approximate solutions of diffusion problems. The theory of the reolprocal problems Is described in both a continuous and discrete context.

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An Analogy Between the Variational Principles of Reactor Theory and those of Classical Mechanics

Publication Date May 01, 1967 by YaSinsky J.B., Kaplan S.

A formal parallelism is shown to exist between two classical variational principles governing the time behavior of mechanical systems and two principles relating to the λ - mode eigenvalue problt'm of neutron group diffusion theory.

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Application of Synthesis Techniques to Problems Involving Time Dependence

Publication Date May 01, 1967 by Kaplan S., Marlowe O.J., Bewick J.

A method described in a previous article (or synthesizing three-dimensional nux distributions is here extended to reactor kinetics problems and to lifetime studies. The method is outlined and some numerical examples presented. The results of these show the method to be a practical way of solving time dependent reactor problems with a detailed spatial model.

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