The Assay of Spatially Random Material pp 170-227 | Cite as
Probabilistic Interpretation of Measurement
Chapter
- 102 Downloads
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.
Keywords
Cost Function Conditional Probability Decision Rule Uranium Deposit Probabilistic Interpretation
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.
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
- [2]For extensive discussion of reaction rates and penetration distributions in pores seeGoogle Scholar
- 1.A. Wheeler, Reaction Rates and Selectivity in Catalyst Pores, in Catalysis, Vol. II, ed. by P. H. Emmett, Reinhold, 1955.Google Scholar
- 2.A. Wheeler and A. J. Robell, Performance of Fixed‐Bed Catalytic Reactors with Poisson in the Feed, J. of Catalysis, 13: 299– 305(1969).CrossRefGoogle Scholar
- [3]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
- [4]See ref. [4] of Chapter 2.Google Scholar
- [5]See ref. [15] no. 1 of Chapter 2.Google Scholar
- [6]J. L. Melsa and D. L. Colin, Decision and Estimation Theory, McGraw‐Hill, 1978.zbMATHGoogle Scholar
- [7]For a fundamental discussion of likelihood ratios seeGoogle Scholar
- J.L. Doob, Stochastic Processes, John Wiley, 1953.zbMATHGoogle Scholar
- For a briefer and simpler treatment see ref. [4] of Chapter 2.Google Scholar
- For a complete statement of Chebyshev’s inequality see:Google Scholar
- G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge University Press, 1951.Google Scholar
- [9] 1.H. L. Van Trees, Detection, Estimation and Modulation Theory, Part I, John Wiley, 1968.zbMATHGoogle Scholar
- 2.See reference [6].Google Scholar
- [10]International Atomic Energy Agency, Technical Reports Series No. 186, Gamma‐Ray Surveys in Uranium Exploration, Vienna, 1979.Google Scholar
- [11] 1.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).CrossRefGoogle Scholar
- 2.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
- [12] 1.Q. Bristow, Airborne Gamma‐Ray Spectrometry in Ura‐nium Exploration. Principles and Current Practice, Int. J. Appl. Rad. Isot., 34: 199 – 229 (1983).CrossRefGoogle Scholar
- For a discussion of the effect of non‐uniformity in the distribution of the radioactive material seeGoogle Scholar
- 2.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
- [13]P. G. Killeen, Borehole Logging for Uranium by Measurement of Natural Gamma‐Radiation, Int. J. Appl. Rad. Isot., 34: 231 – 60 (1983).CrossRefGoogle Scholar
- [14] 1.. D. R. Humphreys et al, Uranium Logging with Prompt Fission Neutrons, Int. J. Appl. Rad. Isot, 34: 261 – 8 (1983).CrossRefGoogle Scholar
- 2.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
- 3.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
- [15]International Atomic Energy Agency, Technical Report Series No. 174, Radiometric Reporting Methods and Calibration in Uranium Exploration, Vienna, 1976.Google Scholar
- [16]Various aspects of vein deposits are discussed in:Google Scholar
- 1.Intl. Atomic Energy Agency Conf. on Vein‐Type and Similar Uranium Deposits in Rocks Younger Than the Proterozoic, Lisbon, 1979.Google Scholar
- In particular, some data on the micro‐structure of such deposits is contained in the paper:Google Scholar
- J. Rimsaite, Chemical and Isotopic Evolution of Radioactive Minerals in Remobilized Vein Type Uranium Deposits, Saskatchewan, Canada, ibid, pp. 35 – 46.Google Scholar
Copyright information
© D. Reidel Publishing Company, Dordrecht, Holland 1985