Theory of Statistics

Schervish, Mark J.

doi:10.1007/978-1-4612-4250-5

Cited by 713 publications

(584 citation statements)

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“…His theorem was a crucial step for Bayesian statistics because it provided the subjective foundation for the parametric statistical model, the basic framework of statistical inference that is based on a set of possible probabilistic models fP g 2 that may govern a given stochastic process, indexed through a parameter space over which there is a prior probability (see, e.g., Kreps, 1988, Schervish, 1995, and Cifarelli and Regazzini, 1996.…”

Section: Ramsey (1926a)mentioning

confidence: 99%

Ambiguity and the Bayesian Paradigm

Gilboa

Marinacci

2016

Readings in Formal Epistemology

168

144

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This is a survey of some of the recent decision-theoretic literature involving beliefs that cannot be quanti…ed by a Bayesian prior. We discuss historical, philosophical, and axiomatic foundations of the Bayesian model, as well as of several alternative models recently proposed. The de…nition and comparison of ambiguity aversion and the updating of non-Bayesian beliefs are brie ‡y discussed. Finally, several applications are mentioned to illustrate the way that ambiguity (or "Knightian uncertainty") can change the way we think about economic problems.

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Section: Ramsey (1926a)mentioning

confidence: 99%

Ambiguity and the Bayesian Paradigm

Gilboa

Marinacci

2016

Readings in Formal Epistemology

168

144

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“…The interval estimate for somatic mutations per Mb tumor DNA represents a ''highest posterior density region'' based on an exact a posteriori analysis, assuming a Poisson model for the distribution of mutations on the genome, and a uniform a priori distribution on the unknown mutation rate (18). It is preferable to standard asymptotic confidence intervals because there are few mutations and the likelihood function is skewed.…”

Section: Determination Of Min Status In Tumor Samplesmentioning

confidence: 99%

Prevalence of somatic alterations in the colorectal cancer cell genome

Wang

Rago

Silliman

et al. 2002

Proc. Natl. Acad. Sci. U.S.A.

167

115

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Although a small fraction of human cancers have increased rates of somatic mutation because of known deficiencies in DNA repair, little is known about the prevalence of somatic alterations in the vast majority of human cancers. To systematically assess nonsynonymous somatic alterations in colorectal neoplasia, we used DNA sequencing to analyze Ϸ3.2 Mb of coding tumor DNA comprising 1,811 exons from 470 genes. In total, we identified only three distinct somatic mutations, comprising two missense changes and one 14-bp deletion, each in a different gene. The accumulation of approximately one nonsynonymous somatic change per Mb of tumor DNA is consistent with a rate of mutation in tumor cells that is similar to that of normal cells. These data suggest that most sporadic colorectal cancers do not display a mutator phenotype at the nucleotide level. They also have significant implications for the interpretation of somatic mutations in candidate tumor-suppressor genes.

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“…Finally, by the asymptotic consistency of Bayes posteriors (see for example Theorem 7.78 of [16] or page 25 of [14]) we see that the RHS of (15) converges to…”

Section: Gpir and The W δmentioning

confidence: 86%