Titlebook: Bayesian Inference; Parameter Estimation Hanns L. Harney Textbook 20031st edition Springer-Verlag Berlin Heidelberg 2003 Bayes Theorem.Data

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談判

,Bayes’ Theorem,of densities and functions are discussed in Sect. 2.2. A symmetry argument can define the prior. This is described in Sects. 2.3 and 2.4. Prior distributions are not necessarily proper. In Sect. 2.5, we comment on improper distributions because it is unusual to admit any of them.

誘騙

POINT

Form Invariance I: Real ,, density discussed in Sect. 2.2. Under a reparameterisation of the hypothesis, the uniform density generally changes into another one that is no longer uniform. If there were a distribution invariant under all transformations, it would be the universal ignorance prior. Such a distribution does not e

瑪瑙

Beyond Form Invariance: The Geometric Prior,ticular, without knowledge of the multiplication function. This is useful because the analysis of the symmetry group may be difficult. This is also of basic importance, since the formula allows one to generalise the definition of the prior distribution to cases where form invariance does not exist.

GLUE

Discrete

Independence of Parameters,l . is assumed here to have two parameters. The way in which the model connects the parameters .. and .. with the set . = (.., ..., ..) of events may be such that it is impossible to integrate over one of them — say .. — and to infer .. individually. The reason is that it may be impossible to define

贊美者

POLYP

Judging a Fit I: Real ,, 13, the function .(.) is actually a family of functions .(.; .), and one determines the range of . that falls into the Bayesian area. It is possible that even the optimum parameter .., defined in Sect. 3.3, yields an inadequate fit. The optimum parameter suggests that one can represent the observed

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