On Bayes’s theorem for improper mixtures
نویسندگان
چکیده
منابع مشابه
On Bayes ’ S Theorem for Improper Mixtures
Although Bayes’s theorem demands a prior that is a probability distribution on the parameter space, the calculus associated with Bayes’s theorem sometimes generates sensible procedures from improper priors, Pitman’s estimator being a good example. However, improper priors may also lead to Bayes procedures that are paradoxical or otherwise unsatisfactory, prompting some authors to insist that al...
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Improper priors are used frequently, but often formally and without reference to a sound theoretical basis. A consequence is the occurrence of seemingly paradoxical results. The most famous example is perhaps given by the marginalization paradoxes presented by Stone and Dawid (1972). It is demonstrated here that the seemingly paradoxical results are removed by a more careful formulation of the ...
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All quantum mixtures are what d’Espagnat has termed “improper.” His “proper” mixture cannot be created — if welcher weg, or distinguishing, information exists, an improper mixture results, while in the absence of such information, the resulting “mixture” is a pure state. D’Espagnat has claimed that an interpretation of the improper mixture in terms of subensembles leads to logical inconsistency...
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This is a complement to the comparison theorem for improper integrals in the textbook. The vanilla version presented in the textbook is good enough to solve some very easy examples and it becomes exponentially gory with the complexity of the integral. Fortunately it is not hard to refine the statement in the book, and turn it into a powerful tool to estimate the convergence of arbitrarily compl...
متن کاملOn Bayes’ Theorem for Improper Mixtures1 by Peter Mccullagh
Although Bayes’s theorem demands a prior that is a probability distribution on the parameter space, the calculus associated with Bayes’s theorem sometimes generates sensible procedures from improper priors, Pitman’s estimator being a good example. However, improper priors may also lead to Bayes procedures that are paradoxical or otherwise unsatisfactory, prompting some authors to insist that al...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2011
ISSN: 0090-5364
DOI: 10.1214/11-aos892