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• W44739198 abstract "THE general problem considered here is that of drawing about a parameter 0, given the observation that the result x of an experiment lies in some set A; a model (X, P, 0) connects x and 0, indexing a family of probability distributions of x over X. Governing these there are indifference principles which may be formulated without a precise statement of the form of the inferences. The best known of these principles is the which states that the inferences about 0 depend only on the likelihood function P(A I 0). This principle has been advocated by Fisher, for example, (1956), Barnard (1949) and others. A recent stimulating contribution by Birnbaum (1962) is accompanied by illuminating discussion. The principle has been the subject of great controversy because it seems to deny the use of concepts involving averages across the sample space, such as unbiasedness. A second type of indifference principle is the which essentially states that refer only to the family of probability distributions on X indexed by 0). Thus if two parameter spaces index the same family of probability distributions, and the observation xe A is made, about the two parameter spaces correspond through the probability distributions they index. The motivation of the present paper lies in studies of the author on determining prior distributions from the model (8,P, 0) (Hartigan, 1964, 1965). These prior distributions depend on the whole model, not merely the likelihood P(A I 0), so the posterior distribution of given x e A does not depend on the likelihood function only. However, the prior distributions do satisfy the invariance principle. The question considered here is whether may be forced to satisfy both the likelihood and invariance principles; we consider, in particular, a form of inference known as an inversion, i.e. a measure over the parameter space given x E A. The likelihood principle and invariance principle together imply the probability principle, which states that about depend only on the probability spectrum .B, the set of values taken by P(A I 0)/sup0P(A I 0); we are forced to make corresponding about any two parameter spaces indexing the same spectrum. We cannot distinguish two 6-values indexing the same point on the spectrum. For inversions which are localizable (i.e. truncation of the parameter space does not essentially change the" @default.
• W44739198 created "2016-06-24" @default.
• W44739198 creator A5005877049 @default.
• W44739198 date "1967-09-01" @default.
• W44739198 modified "2023-09-26" @default.
• W44739198 title "The Likelihood and Invariance Principles" @default.
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• W44739198 doi "https://doi.org/10.1111/j.2517-6161.1967.tb00715.x" @default.
• W44739198 hasPublicationYear "1967" @default.
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