Quantum theory and the bayesian inference problems
Many physicists take it for granted that their theories can be either refuted or verified by comparison with experimental data. In order to evaluate such data, however, one must employ statistical estimation and inference methods which, unfortunately, always involve an ad hoc proposition. The nature of the latter depends upon the statistical method adopted; in the Bayesian approach, for example, one must usesome Lebesgue measure in the “set of all possible distributions.” The ad hoc proposition has usually nothing in common with the physical theory in question, thus subjecting its verification (or refutation) to further doubt. This paper points out one notable exception to this rule. It turns out that in the case of the quantum mechanical systems associated with finite-dimensional Hilbert spaces the proposition is completely determined by the premises of the quantum theory itself.
Key wordsQuantum theory statistical inference Bayesian inference
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- 3.A. N. Kolmogorov,Foundations of the Theory of Probability, Chelsea, New York (1956), Chapter I.Google Scholar
- 2.T. Bayes,Phil. Trans. 53:376 (1763); reproduced, accompanied by a biographical note by G. A. Barnard, inBiometrica 45:293 (1958); also in E. S. Pearson and M. G. Kendall,Studies in the History of Statistics and Probability, Hafner, Darien, Connecticut (1970).Google Scholar
- 3.M. G. Kendall and W. R. Buckland,A Dictionary of Statistical Terms, Oliver and Boyd, Edinburgh (1957).Google Scholar
- 4.H. Freeman,Introduction to Statistical Inference, Addison-Wesley, Reading, Massachusetts (1963).Google Scholar
- 5.R. Von Mises,Math. Z. 4:1 (1919).Google Scholar
- 6.R. Von Mises,Ann. Math. Slat. 13:156 (1942).Google Scholar
- 7.R. Von Mises,Mathematical Theory of Probability and Statistics (collection edited by H. Geiringer), Academic Press, New York (1964).Google Scholar
- 8.W. Feller,An Introduction to Probability Theory and its Applications, Wiley, New York (1968), Vol. I, Chapter V.Google Scholar
- 9.M. G. Kendall and A. Stuart,The Advanced Theory of Statistics, C. Griffin and Co., London (1961), Chapter 31.Google Scholar
- 10.P. J. Huber,Ann. Math. Stat. 43:1041 (1972).Google Scholar