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Statistical Decision Theory and Bayesian Analysis
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TLDR
An overview of statistical decision theory, which emphasizes the use and application of the philosophical ideas and mathematical structure of decision theory.Abstract:
1. Basic concepts 2. Utility and loss 3. Prior information and subjective probability 4. Bayesian analysis 5. Minimax analysis 6. Invariance 7. Preposterior and sequential analysis 8. Complete and essentially complete classes Appendices.read more
Citations
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Journal ArticleDOI
A model-averaging method for assessing groundwater conceptual model uncertainty.
TL;DR: This study shows that contribution of model uncertainty to predictive uncertainty is significantly larger than that of parametric uncertainty for the recharge and geological components of the Death Valley Regional Flow System.
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New Procedures to Select the Best Simulated System Using Common Random Numbers
Stephen E. Chick,Koichiro Inoue +1 more
TL;DR: New two-stage procedures that use common random numbers to help identify the best simulated system to reduce either the expected opportunity cost associated with potentially selecting an inferior system, or the probability of incorrect selection are presented.
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Ranges of posterior measures for priors with unimodal contaminations
Siva Sivaganesan,James O. Berger +1 more
TL;DR: In this paper, the authors consider the problem of robustness or sensitivity of given Bayesian posterior criteria to specification of the prior distribution, including the posterior mean, variance and probability of a set (for credible regions and hypothesis testing).
Journal ArticleDOI
Quantifying uncertainty in climate change science through empirical information theory
Andrew J. Majda,Boris Gershgorin +1 more
TL;DR: An information metric to quantify AOS model errors in the climate is proposed here which incorporates both coarse-grained mean model errors as well as covariance ratios in a transformation invariant fashion.
Bayes factors and marginal distributions in invariant situations
TL;DR: In this article, the marginal density of a "minimal" data set is typically available in closed form, regardless of the error distribution, and the conditions for the results to hold are explored in some detail for nonnormal linear models and various transformations thereof.