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- W32406506 abstract "Let θ represent the unobservable parameter of a sampling model f(x|θ) and ϕ(θ) the quantity of interest. In this article ranges of the posterior expectation of ϕ(θ), as the prior for θ varies over some commonly used classes of prior distributions, are studied. This kind of study is termed “global” Bayesian robustness of the class of priors for the quantity ip(0). In this paper attention is paid to the methodology for finding these ranges and the prior distributions at which the extreme values are attained. We shall consider contamination classes of prior distributions of a specified prior π0(θ), corresponding to various contaminating classes. Contaminating classes include the class of priors having some “quantiles” as those of π0(θ), the class with “shape” and quantile constraints compatible with π0(θ), and the class with marginals as those of π0(θ). Extensions of contamination classes -mainly proposed for modeling local uncertainty on π0(θ), and for studying influence sets to guide an interactive robust analysis — are also reviewed. The class of priors with given marginals plays an important role in multidimensional parameter spaces: this class contains any possible conditional distribution among the components, but maintains fixed the one-dimensional marginals. The main developments, which are based on the generalized moment constraints classes, are discussed. The class of probability densities in a given “band” has interesting properties: it allows us to model with considerable freedom the tail behavior of θ and is the underlying class in the theory of precise measurement. The main results related to this class are also reviewed." @default.
- W32406506 created "2016-06-24" @default.
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- W32406506 date "2000-01-01" @default.
- W32406506 modified "2023-09-27" @default.
- W32406506 title "Global Bayesian Robustness for Some Classes of Prior Distributions" @default.
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- W32406506 doi "https://doi.org/10.1007/978-1-4612-1306-2_3" @default.
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