zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Sensitivity in Bayesian statistics: The prior and the likelihood. (English) Zbl 0734.62005
Summary: One paradigm for sensitivity analyses in Bayesian statistics is to specify $\Gamma$, a reasonable class of priors, and to compute the corresponding class of posterior inferences. The class $\Gamma$ is chosen to represent uncertainty about the prior. There is often additional uncertainty, however, about the family of sampling distributions. This article introduces a method for computing ranges of posterior expectations over reasonable classes of sampling distributions that lie “close to” a given parametric family. By treating the prior as a probability measure on the space of sampling distributions this article also gives a unified treatment to what are usually considered two separate problems - sensitivity to the prior and sensitivity to the sampling model. First the notion of “close to” is made explicit. Then, an algorithm is given for turning ratio-linear problems into sequences of linear problems. In addition to solving the problem at hand, the algorithm simplifies many other robust Bayesian computational problems. Finally, the method is illustrated with an example.

62A01Foundations and philosophical topics in statistics
65C99Probabilistic methods, simulation and stochastic differential equations (numerical analysis)
62F15Bayesian inference
Full Text: DOI