The case for objective Bayesian analysis

By James O. Berger. 2006

733 citations recorded by the source corpus.

Bayesian statistical practice makes extensive use of versions of ob- jective Bayesian analysis. We discuss why this is so, and address some of the criticisms that have been raised concerning objective Bayesian analysis. The dan- gers of treating the issue too casually are also considered. In particular, we suggest that the statistical community should accept formal objective Bayesian techniques with confldence, but should be more cautious about casual objective Bayesian techniques.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d1d875e9f7020ee98f5a1051c2a567cba52299d1

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In Statistics and Probability

Citations in the corpus

Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression (2016, background): “Another branch of the literature encouraged the choice of ‘objective’ priors (Bernardo, 1979; Berger, 2006; Ghosh, 2011) or Jeffreys priors (Berger et al., 2009).”
Bayesian Analysis of Factorial Designs (2017, methodology): “We advocate the use of Bayes factors which provide a principled approach for stating evidence from data for competing models (Berger & Sellke, 1987; Edwards, Lindman, & Savage, 1963; Jeffreys, 1961; Morey, Romeijn, & Rouder, 2013; Raftery, 1995). There are two pragmatic advantages of Bayes factors f”
Foundations of Linear and Generalized Linear Models (2015, background): “As a prerequisite, the reader should be familiar with basic theory of statistics, such as presented by Casella and Berger (2001). Although not mandatory, it will be helpful if readers have at least some background in applied statistical modeling, including linear regression and ANOVA.”
On Some Principles of Statistical Inference (2015, methodology): “A lively discussion of calibration of Bayesian approaches is given from several points of view by Berger (2006), Goldstein (2006), Browne & Draper (2006) and extensive discussions.”
Marginal Inferential Models: Prior-Free Probabilistic Inference on Interest Parameters (2013, methodology): “2011), and Bayesian inference with default, reference, or data-dependent priors (Berger 2006; Berger et al. 2009; Fraser 2011; Fraser et al. 2010). The key idea behind Fisher’s fiducial argument is to write the sampling model in terms of an auxiliary variable U with known distribution PU , and then ”
Beyond subjective and objective in statistics (2015, background): “Some Bayesians (notably Jaynes (2003) and Berger (2006)) have advocated an objective approach, whereas others (notably de Finetti (1974)) have embraced subjectivity.”
Approximate Bayesian Computation (2013, background): “However, theoretical results regarding objective priors are available, which may for example be based on the principle of indifference or the principle of maximum entropy [43,44].”
Bayesian Estimation and Inference (2015, background): “This is why Bayesian and frequentist estimates converge when priors are uninformative: Likelihoods dominate posteriors (Berger, 2006).”
A Comparison of Bayes–Laplace, Jeffreys, and Other Priors (2008, result): “L prior as a consensus prior, with the caveat that all four “plausible” priors (Berger 1985) will give highly similar results for 0 x n. [Received February 2007.”
A Default Bayesian Hypothesis Test for ANOVA Designs (2012, methodology): “In this scenario, the main difficulty with the Bayes factor is its sensitivity to the prior distribution for the model parameters under test (Press et al. 2003; Berger 2006; Gelman 2008).”
A note on p-values interpreted as plausibilities (2012, methodology): “2011), Dempster–Shafer theory (Dempster 2008; Shafer 1976, 2011), generalized p-values and confidence intervals (Chiang 2001; Tsui and Weerahandi 1989; Weerahandi 1993), and Bayesian inference with default, reference, and/or data-dependent priors (Berger 2006; Berger et al. 2009; Fraser 2011; Fraser”