Objections to Bayesian statistics

By Andrew Gelman. 2008

237 citations recorded by the source corpus.

Bayesian inference is one of the more controversial approaches to statistics. The fundamental objections to Bayesian methods are twofold: on one hand, Bayesian methods are presented as an automatic inference engine, and this raises suspicion in anyone with applied experience. The second objection to Bayes comes from the opposite direction and addresses the subjective strand of Bayesian inference. This article presents a series of objections to Bayesian inference, written in the voice of a hypothetical anti-Bayesian statistician. The article is intended to elicit elaborations and extensions of these and other arguments from non-Bayesians and responses from Bayesians who might have dieren t perspectives on these is- sues.

Subfields: Artificial Intelligence, Statistics and Probability

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

Weight Uncertainty in Neural Networks (2015, background): “Changing the prior based upon the data that it is meant to regularise is known as empirical Bayes and there is much debate as to its validity (Gelman, 2008).”
Prior sensitivity in theory testing: An apologia for the Bayes factor (2010, background): “The prior sensitivity of the marginal likelihood has not only been lamented in statistics (e.g., Aitkin, 1991; Bayarri & Berger, 2000; Efron, 1986; Gelman, 2008; Kass, 1993; O’Hagan, 1995; Wasserman, 1996), but also in more applied fields like sociology (e.g., Xie, 1999), marketing (e.g., Rossi &…”
Probabilistic rainfall thresholds for landslide occurrence using a Bayesian approach (2012, unknown): “[60] Critics of Bayesian methods complain that Bayes rule does not tell us anything we didn’t already believe [Gelman, 2008].”
Testing hypotheses via a mixture estimation model (2014, background): “INTRODUCTION Hypothesis testing is one of the central problems of statistical inference and a dramatically differentiating feature of classical and Bayesian paradigms (Neyman and Pearson, 1933; Berger and Sellke, 1987; Casella and Berger, 1987; Gigerenzer, 1991; Berger, 2003; Mayo and Cox, 2006; Gel”
Weight Uncertainty in Neural Network (2015, background): “Changing the prior based upon the data that it is meant to regularise is known as empirical Bayes and there is much debate as to its validity (Gelman, 2008).”
Self-supervised calibration for robotic systems (2013, background): “The use of priors is still subject to controversial discussions [30] between Bayesian and non-Bayesian statisticians.”
Generalized Out-of-Distribution Detection: A Survey (2021, unknown): “However, their obvious shortcomings of inaccurate predictions [303] and high computational costs [304] prevent them from wide adoption in practice.”
Simulation-based optimal Bayesian experimental design for nonlinear systems (2011, background): “(For discussions contrasting Bayesian and frequentist approaches to statistics, see [27] and [28].”
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).”