Skip to main content

Probabilistic Interpretation of Measurement

  • Chapter
  • 151 Accesses

Part of the book series: Mathematics and Its Applications ((MAIA,volume 20))

Abstract

The previous two Chapters were devoted to developing an efficient computerizable algorithm for evaluating a deterministic measure of performance. We found that this criterion can be used to quantitatively compare alternative assay-system designs. By such comparison one can seek to optimize the number of detectors and their deployment around the sample as well as other related design parameters. However, the deterministic criterion makes no distinction between likely and unlikely spatial distributions of source material in the sample. As a consequence, we concluded that the deterministic measure of performance tends to give a conservative estimate of the relative mass resolution. Its utility is the speed and simplicity with which one may compare a large number of assay-system designs.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F. A. Fry, B. M. R. Green, A. Knight and D. R. White, A Realistic Chest Phantom for the Assessment of Low Energy Emitters in Human Lungs, 4‐th Intl. Conf. of the Intl. Rad. Protection Soc., Vol. 2, pp 475‐8, Paris, 1977.

    Google Scholar 

  2. W. W. Parkinson, jr., R. E. Goans and W. M. Good, Realistic Calibration of Whole‐Body Counters for Measuring Plutonium, Intl. Atomic Energy Agency, Conf. on Natl, and Intl. Standardization of Rad. Dosimetry, Vol. Ill, pp 155–66, Vienna, 1977.

    Google Scholar 

  3. For extensive discussion of reaction rates and penetration distributions in pores see

    Google Scholar 

  4. A. Wheeler, Reaction Rates and Selectivity in Catalyst Pores, in Catalysis, Vol. II, ed. by P. H. Emmett, Reinhold, 1955.

    Google Scholar 

  5. A. Wheeler and A. J. Robell, Performance of Fixed‐Bed Catalytic Reactors with Poisson in the Feed, J. of Catalysis, 13: 299– 305(1969).

    Article  Google Scholar 

  6. This assumption is physically reasonable since the response function is expected to be continuous and smooth. However, if the probability density does not exist the only alteration needed in our subsequent derivation is that the integrals involving the probability density must be changed to Lebesque integrals with the probability distribution P as the measure.

    Google Scholar 

  7. See ref. [4] of Chapter 2.

    Google Scholar 

  8. See ref. [15] no. 1 of Chapter 2.

    Google Scholar 

  9. J. L. Melsa and D. L. Colin, Decision and Estimation Theory, McGraw‐Hill, 1978.

    MATH  Google Scholar 

  10. For a fundamental discussion of likelihood ratios see

    Google Scholar 

  11. J.L. Doob, Stochastic Processes, John Wiley, 1953.

    MATH  Google Scholar 

  12. For a briefer and simpler treatment see ref. [4] of Chapter 2.

    Google Scholar 

  13. For a complete statement of Chebyshev’s inequality see:

    Google Scholar 

  14. G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge University Press, 1951.

    Google Scholar 

  15. H. L. Van Trees, Detection, Estimation and Modulation Theory, Part I, John Wiley, 1968.

    MATH  Google Scholar 

  16. See reference [6].

    Google Scholar 

  17. International Atomic Energy Agency, Technical Reports Series No. 186, Gamma‐Ray Surveys in Uranium Exploration, Vienna, 1979.

    Google Scholar 

  18. T. W. Parker, Determination of the Concentration of Uranium in Soil and Stream Sediment Samples Using a High Resolution Energy‐Dispersive X‐Ray Fluorescence Analyzer, Int. J. Appl. Rad. Isot., 34: 273 – 81 (1983).

    Article  Google Scholar 

  19. J. K. Osmond, J. B. Cowart and M. Ivanovich, Uranium Isotope Disequilibrium in Ground Water as an Indicator of Anomalies, ibid, pp. 283–308.

    Google Scholar 

  20. Q. Bristow, Airborne Gamma‐Ray Spectrometry in Ura‐nium Exploration. Principles and Current Practice, Int. J. Appl. Rad. Isot., 34: 199 – 229 (1983).

    Article  Google Scholar 

  21. For a discussion of the effect of non‐uniformity in the distribution of the radioactive material see

    Google Scholar 

  22. M. R. Wormald and C. G. Clayton, Observations on the Ac‐curacy of Gamma Spectrometry in Uranium Prospecting, Intl. Atomic Energy Agency Conf. on Exploration for Uranium Ore Deposits, Vienna, 1976, pp. 147 – 71.

    Google Scholar 

  23. P. G. Killeen, Borehole Logging for Uranium by Measurement of Natural Gamma‐Radiation, Int. J. Appl. Rad. Isot., 34: 231 – 60 (1983).

    Article  Google Scholar 

  24. . D. R. Humphreys et al, Uranium Logging with Prompt Fission Neutrons, Int. J. Appl. Rad. Isot, 34: 261 – 8 (1983).

    Article  Google Scholar 

  25. L. A. Shope et al, The Operation and Life of the Zetatron Neutron Tube in a Borehole Logging Application, ibid, pp. 269–72.

    Google Scholar 

  26. M. R. Wormald and C. G. Clayton, Some Factors Affecting Accuracy in the Direct Determination of Uranium by Delayed Neutron Borehole Logging, Intl. Atomic Energy Agency Conf. on Exploration for Uranium Ore Deposits, Vienna, 1976, pp. 427 – 70.

    Google Scholar 

  27. International Atomic Energy Agency, Technical Report Series No. 174, Radiometric Reporting Methods and Calibration in Uranium Exploration, Vienna, 1976.

    Google Scholar 

  28. Various aspects of vein deposits are discussed in:

    Google Scholar 

  29. Intl. Atomic Energy Agency Conf. on Vein‐Type and Similar Uranium Deposits in Rocks Younger Than the Proterozoic, Lisbon, 1979.

    Google Scholar 

  30. In particular, some data on the micro‐structure of such deposits is contained in the paper:

    Google Scholar 

  31. J. Rimsaite, Chemical and Isotopic Evolution of Radioactive Minerals in Remobilized Vein Type Uranium Deposits, Saskatchewan, Canada, ibid, pp. 35 – 46.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1985 D. Reidel Publishing Company, Dordrecht, Holland

About this chapter

Cite this chapter

Ben-Haim, Y. (1985). Probabilistic Interpretation of Measurement. In: The Assay of Spatially Random Material. Mathematics and Its Applications, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5422-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-5422-9_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8893-0

  • Online ISBN: 978-94-009-5422-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics