The interplay of Bayesian and frequentist analysis

By Maria J. Bayarri, James O. Berger. 2004

536 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/98876f482ae9828c6b7153a92bad949c2af36571

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Bayesian analysis of measurement error models using integrated nested Laplace approximations (2015, background): “It is often of interest to study frequentist properties of Bayesian estimates (Bayarri and Berger, 2004).”
Integrated Sensing and Communications: Recent Advances and Ten Open Challenges (2023, background): “We remark that the CRB and BCRB/PCRB represent different perspectives in statistics, which constitute fundamental philosophical and cognitive issues [145].”
The semiparametric Bernstein-von Mises theorem (2010, methodology): “Endow Θ with a thick prior and C[0, 1] with a prior ΠH without pointmasses, such that H ⊂ supp(ΠH).”
Valid P-Values Behave Exactly as They Should: Some Misleading Criticisms of P-Values and Their Resolution With S-Values (2019, background): “…if it is uniformly distributed when H and A are correct; in that case, for every α the rule “reject H when p ≤ α” will falsely reject H with frequency α (Bayarri and Berger 2004).2 Of course, issues of power must enter into choice of the test statistic from which p is computed, but those…”
The best inflationary models after Planck (2013, background): “[19, 20] for a discussion of issues in Bayesianfrequentist calibrations).”
Diagnostics of prior-data agreement in applied Bayesian analysis (2008, background): “As Bayarri and Berger 8 9 recommend, p -values must be carefully used; the understanding of the result could thus be mistaken for industrial analysts that are not statisticians.”
Philosophy and the practice of Bayesian statistics (2010, unknown): “…the 10There is some controversy in the literature about whether posterior predictive checks have too little power to be useful statistical tools (Bayarri and Berger, 2000, 2004), how they might be modified to increase their power (Robins et al., 2000; Fraser and Rousseau, 2008), whether some…”
Information, Divergence and Risk for Binary Experiments (2009, background): “There are several works (Barnett, 1999; Bayarri and Berger, 2004; Berger, 2003) that compare and contrast these.”
Weak Identifiability in Models for Mark-Recapture-Recovery Data (2009, background): “... correlations between parameters in the posterior distribution, which in turn implies poor mixing in the MCMC samples and very slow convergence (Carlin and Louis 1996; Rannala 2002); even with large sample sizes, the likelihood may be unable to overcome the prior (Neath and Samaniego 1997); a too”
Assessing Mediational Models: Testing and Interval Estimation for Indirect Effects (2010, background): “For more extensive discussion of the differences between these perspectives see Bayarri and Berger (2004) .”
QuantiSNP: an Objective Bayes Hidden-Markov Model to detect and accurately map copy number variation using SNP genotyping data (2007, methodology): “In instances where little or no substantive prior knowledge is available, the Objective Bayes approach provides a principled method to set parameters of the priors; such that the resulting Bayesian procedures possess good long-run frequency properties (29) (for general discussion of Objective Bayes ”
The case for objective Bayesian analysis (2006, background): “Bayarri and Berger (2004) review the vast literature showing that objective Bayesian methods are the most promising route to the unification of Bayesian and frequentist statistics.”
Why P Values Are Not a Useful Measure of Evidence in Statistical Significance Testing (2008, background): “The upshot is that many researchers (e.g., Bayarri & Berger, 1999, 2000, 2004; Berger, 2003; Berger & Sellke, 1987; Gigerenzer, 1993; Goodman, 1993, 1999; Hubbard, 2004; Hubbard & Bayarri, 2003a, 2003b, 2005) state that the p value is routinely misinterpreted as a frequentist Type I error…”
Neutral noninformative and informative conjugate beta and gamma prior distributions (2011, background): “Most practitioners are however probably more interested in the average performance rather than the worst possible performance over a sequence of trials [1, 3].”
Posterior propriety and admissibility of hyperpriors in normal hierarchical models (2005, background): “The most successful approach to evaluation of objective improper priors has been to study the frequentist properties of the ensuing Bayes procedures (see [3] for discussion and many references).”