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# Philosophy and the practice of Bayesian statistics.

### Author information

- 1
- Department of Statistics and Department of Political Science, Columbia University, New York, New York 10027, USA. gelman@stat.columbia.edu

### Abstract

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework.

© 2012 The British Psychological Society.

### Comment in

- Posterior predictive checks can and should be Bayesian: comment on Gelman and Shalizi, 'Philosophy and the practice of Bayesian statistics'. [Br J Math Stat Psychol. 2013]
- Comment on Gelman and Shalizi. [Br J Math Stat Psychol. 2013]
- How to practise Bayesian statistics outside the Bayesian church: what philosophy for Bayesian statistical modelling? [Br J Math Stat Psychol. 2013]
- The humble Bayesian: model checking from a fully Bayesian perspective. [Br J Math Stat Psychol. 2013]
- Rejoinder to discussion of 'Philosophy and the practice of Bayesian statistics'. [Br J Math Stat Psychol. 2013]
- The error-statistical philosophy and the practice of Bayesian statistics: comments on Gelman and Shalizi: 'Philosophy and the practice of Bayesian statistics'. [Br J Math Stat Psychol. 2013]

- PMID:
- 22364575
- PMCID:
- PMC4476974
- DOI:
- 10.1111/j.2044-8317.2011.02037.x

- [Indexed for MEDLINE]