Advertisement

Probabilistic Design

  • Yakov Ben-Haim
Chapter
  • 101 Downloads
Part of the Mathematics and Its Applications book series (MAIA, volume 20)

Abstract

In the previous three Chapters we have studied assay-system design and measurement-interpretation as separate tasks in the assay of spatially random materials. In Chapters 2 and 3 we developed and generalized the concept of relative resolution as a measure of performance. The relative resolution is a deterministic design tool in the sense that it accounts for all allowed spatial distributions of the analyte, without consideration of the relative probability of different distributions. The relative resolution is a concise physically meaningful quantity, and it can be formulated algorithmically for convenient computation. In Chapter 4 we turned our attention from assay-system design to probabilistic interpretation of measurement. The basic tool in probabilistic analysis is the conditional probability density. We studied the construction of conditional densities, and we found that extensive stochastic information about the assay problem is required, as well as considerable computational effort.

Keywords

Measurement Vector Probabilistic Design Conditional Density Conditional Probability Density Source Particle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    This inequality was first formulated by R. A. Fisher inGoogle Scholar
  2. 1.
    R. A. Fisher, On the Mathematical Foundations of Theoretical Statistics, Proc. Roy. Soc., London, 222: 309 (1922).Google Scholar
  3. However, this Theorem is usually associated with the work of Rao and Cramer:Google Scholar
  4. 2.
    R. Rao, Information and Accuracy Attainable in the Estimation of Statistical Parameters, Bull. Calcutta Math. Soc., 37: 81 – 91 (1945).MathSciNetzbMATHGoogle Scholar
  5. 3.
    H. Cramer, Mathematical Methods of Statistics, Princeton Univ. Press, 1946.zbMATHGoogle Scholar
  6. The Theorem is discussed in many standard texts, includingGoogle Scholar
  7. 4.
    . R. V. Hogg and A. T. Craig, Introduction to Mathematical Statistics, Macmillan, 1970.Google Scholar
  8. [2]
    For a general discussion of sequential analysis seeGoogle Scholar
  9. 1.
    H. Chernoff, Sequential Analysis and Optimal Design, S.I.A.M. monograph, 1972.Google Scholar
  10. Applications of sequential analysis in the assay of nuclear materials are discussed inGoogle Scholar
  11. 2.
    P. E. Fehlau, K. L. Coop and K. V. Nixon, Sequential Probability Ratio Controllers for Safeguards Radiation Monitors, 6‐th ESARDA Symp. on Safeguards and Nuclear Mat. Mgt., pp 155–7, Venice, May 1984.Google Scholar
  12. 3.
    P. E. Fehlau, K. L. Coop and J. T. Markin, Applications of Wald’s Sequential Probability Ratio Test to Nuclear Materials Control, ESARDA Specialist’s Working Group on Statistical Problems in Nondestructive Assay, Ispra, Italy, Sept. 1984.Google Scholar
  13. [3]
    Y. L. Tong, Probability Inequalities in Multivariate Distributions, Academic Press, 1980.zbMATHGoogle Scholar
  14. [4]
    Y. Ben‐Haim, Convex Sets and Nondestructive Assay, S. I. A. M. J. Algebraic and Discrete Methods, to appear.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1985

Authors and Affiliations

  • Yakov Ben-Haim
    • 1
  1. 1.Department of Nuclear EngineeringTechnion-Israel Institute of TechnologyIsrael

Personalised recommendations