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Statistical Decision Theory and Bayesian Analysis
An overview of statistical decision theory, which emphasizes the use and application of the philosophical ideas and mathematical structure of decision theory. The text assumes a knowledge of basic
Optimal predictive model selection
It is shown that, for selection among normal linear models, the optimal predictive model is often the median probability model, which is defined as the model consisting of those variables which have overall posterior probability greater than or equal to 1/2 of being in a model.
Mixtures of g Priors for Bayesian Variable Selection
Zellner's g prior remains a popular conventional prior for use in Bayesian variable selection, despite several undesirable consistency issues. In this article we study mixtures of g priors as an
The Intrinsic Bayes Factor for Model Selection and Prediction
This article introduces a new criterion called the intrinsic Bayes factor, which is fully automatic in the sense of requiring only standard noninformative priors for its computation and yet seems to correspond to very reasonable actual Bayes factors.
Redefine statistical significance
The default P-value threshold for statistical significance is proposed to be changed from 0.05 to 0.005 for claims of new discoveries in order to reduce uncertainty in the number of discoveries.
Testing a Point Null Hypothesis: The Irreconcilability of P Values and Evidence
Abstract The problem of testing a point null hypothesis (or a “small interval” null hypothesis) is considered. Of interest is the relationship between the P value (or observed significance level) and
Testing Precise Hypotheses
Testing of precise (point or small interval) hypotheses is reviewed, with special emphasis placed on exploring the dramatic conflict between conditional measures (Bayes factors and posterior
The case for objective Bayesian analysis
It is suggested that the statistical community should accept formal objective Bayesian techniques with confidence, but should be more cautious about casual objectiveBayesian techniques.
Objective Bayesian Analysis of Spatially Correlated Data
Spatially varying phenomena are often modeled using Gaussian random fields, specified by their mean function and covariance function. The spatial correlation structure of these models is commonly