Is Bayes Posterior just Quick and Dirty Confidence

By Donald Fraser. 2011

138 citations recorded by the source corpus.

Bayes (1763) introduced the observed likelihood function to statistical inference and pro- vided a weight function to calibrate the parameter; he also introduced a condence results were dierent when the model was not location. This paper examines the occurrence of true statements from the Bayes approach and from the condence approach, and shows that the proportion of true statements in the Bayes case depends critically on the presence of linearity in the model; and with departure from this linearity the Bayes approach can be seriously misleading. Bayesian integration of weighted likelihood provides a rst order linear approximation to condence, but without linearity can give substantially incorrect results.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/23ac3ccb45e689cee5b01e6106f820688a9af752

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In Applied Mathematics

In Statistics and Probability

Citations in the corpus

The expected demise of the Bayes factor (2015, background): “(This difficulty is not to be confused with the divergence in the [frequentist versus epistemic] interpretations of the probability statement, as discussed in Fraser (2011) and the ensuing comments.) At a different semantic level, the long-going [or long-winded] criticism on the Bayesian approach, n”
A note on p-values interpreted as plausibilities (2012, background): “This is perhaps not surprising given that objective Bayes posterior distributions can be viewed as a simple and attractive way to approximate frequentist p-values (Fraser 2011).”
On Some Principles of Statistical Inference (2015, background): “This is increasingly questionable as the dimension of the parameter space increases, as it leads to well-established difficulties with marginalisation and with calibration (Dawid et al., 1973; Fraser, 2011).”
Uncertainty Quantification for the Horseshoe (with Discussion) (2016, background): “For example, even in apparently simple fixed-dimensional problems, Fraser (2011) and Fraser et al. (2016) describe situations where Bayesian uncertainty quantification is less than fully satisfactory.”
An imprecise-probabilistic characterization of frequentist statistical inference (2021, background): “Confidence is a fundamental concept in statistics, “arguably the most substantive ingredient in modern model-based theory” (Fraser 2011b), dating back to Neyman (1941) and also, indirectly, to Fisher through its close ties to fiducial inference (Efron 1998; Zabell 1992).”
Marginal Inferential Models: Prior-Free Probabilistic Inference on Interest Parameters (2013, methodology): “Likelihood-based solutions were presented by Fraser, Reid, and Wong (1997), and Kulkarni and Powar (2010) took a different approach.”
Generalized Fiducial Inference: A Review and New Results (2016, background): “Another related approach is based on higher order likelihood expansions and implied data-dependent priors (Fraser 2004, 2011; Fraser, Reid, and Wong 2005; Fraser and Naderi 2008; Fraser, Fraser, and Staicu 2009; Fraser et al. 2010).”