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Van Fraassen [9J has shown how to extend 'simple' conditional probabilities to compounds containing conditionals in such a way as to satisfy the Kolmogorov axioms, but David Lewis [8J has shown that this cannot be done if the rule that probabilities change by conditionalization is also to be satisfied. 4 The correctness of the conditional probability measure of conditionals' probabilities, though perhaps intuitively plausible, can itself be debated. David Lewis [8J, for example, argues that conditional probabilities measure only the propriety of asserting a conditional, but not the rationality of accepting it.

0, P) be a simple probability model. There are occasions where one does not observe outcomes directly but can measure only something about those outcomes. ) , Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. [, 23-28, All Rights Reserved, Copyright © 1976 by D, Reidel Publishing Company, Dordrecht-Holland, 24 P. D. {. {-valued random variable on Q but we will say that it is a measurement function on Q. For any 'subset'S of Q write P(S)= I P(w) roES with the convention that when S= D, the empty set, one has P(D)=O.

Wiley, New York, p. 5, 1963. [IIJ B. ), Chelsea, Bronx, pp. 54-55, 1968. [12] E. Parzen, Modern Probability Theory and Its Applications, Wiley, New York, p. 2, 1960. [13] C. P. Schnorr, Zufalligskeit und Wahrscheinlichkeit, Springer-Verlag, Berlin, New York,1971. [14] T. M. Cover, private communication. [15] G. J. Chaitin, 'Information-Theoretic Computational Complexity', IEEE Trans. on Information Theory, IT-20, 10-15, 1974. [16] E. Hewitt and L. J. Savage, 'Symmetric Measures on Cartesian Products', Trans.

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A case study in non-centering for data augmentation: Stochastic epidemics by Neal P.

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