Conditional probability and improper priors
نویسندگان
چکیده
منابع مشابه
Improper Priors Are Not Improper
It is well known that improper priors in Bayesian statistics may lead to proper posterior distributions and useful inference procedures. This motivates us to give an elementary introduction to a theoretical frame for statistics that includes improper priors. Axioms that allow improper priors are given by a relaxed version of Kolmogorov’s formulation of probability theory. The theory of conditio...
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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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At the bottom of page 1614, we are not precise in the definition of a Borel space. The condition should have read that there is a one-to-one measurable function with measurable inverse between (Ω,B) and (E,E), where E is a Borel subset of the reals and E is the Borel σ-field of subsets of E. After the remaining corrections below, our use of the term “Borel space” conforms with this definition. ...
متن کاملLexicographic probability, conditional probability, and nonstandard probability
The relationship between Popper spaces (conditional probability spaces that satisfy some regularity conditions), lexicographic probability systems (LPS’s) [Blume, Brandenburger, and Dekel 1991a; Blume, Brandenburger, and Dekel 1991b], and nonstandard probability spaces (NPS’s) is considered. If countable additivity is assumed, Popper spaces and a subclass of LPS’s are equivalent; without the as...
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ژورنال
عنوان ژورنال: Communications in Statistics - Theory and Methods
سال: 2016
ISSN: 0361-0926,1532-415X
DOI: 10.1080/03610926.2014.935430