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Probability Matching Priors: Higher Order Asymptotics

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TLDR
In this paper, the shrinkage argument was used to match the prior for distribution functions and for prediction in the case of posterior density regions, and for other credible regions for prediction.
Abstract
Introduction and the Shrinkage Argument.- Matching Priors for Posterior Quantiles.- Matching Priors for Distribution Functions.- Matching Priors for Highest Posterior Density Regions.- Matching Priors for Other Credible Regions.- Matching Priors for Prediction.

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The case for objective Bayesian analysis

James O. Berger
- 01 Sep 2006 - 
TL;DR: It is suggested that the statistical community should accept formal objective Bayesian techniques with confidence, but should be more cautious about casual objectiveBayesian techniques.
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The formal definition of reference priors

TL;DR: It is shown how an explicit expression for the reference prior can be obtained under very weak regularity conditions and used to derive new reference priors both analytically and numerically.
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The formal definition of reference priors

TL;DR: Reference analysis produces objective Bayesian inference, in the sense that inferential statements depend only on the assumed model and the available data, and the prior distribution used to make an inference is least informative in a certain information-theoretic sense.
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Assessing Mediational Models: Testing and Interval Estimation for Indirect Effects

TL;DR: An extensive Monte Carlo simulation evaluating a host of approaches for assessing mediation suggests that the new inferential method—the partial posterior p value—slightly outperforms existing ones in terms of maintaining Type I error rates while maximizing power, especially with incomplete data.
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