The error‐statistical philosophy and the practice of Bayesian statistics: Comments on Gelman and Shalizi: ‘Philosophy and the practice of Bayesian statistics’

I am pleased to have the opportunity to comment on this interesting and provocative paper. I shall begin by citing three points on which the authors happily depart from existing work on statistical foundations. First, there is the authors’ recognition that methodology is ineluctably bound up with philosophy. ‘If nothing else, ... strictures derived from philosophy can inhibit research progress’ (Gelman& Shalizi, 2013, p. 11). They note, for example, the reluctance of some Bayesians to test their models because of their belief that ‘Bayesian models were by definition subjective’, or perhaps because checking involves non-Bayesian methods (p. 4, n. 4). Second, they recognize that Bayesian methods need a new foundation. Although the subjective Bayesian philosophy, ‘strongly influenced by Savage (1954), is widespread and influential in the philosophy of science (especially in the form of Bayesian confirmation theory...)’, and while many practitioners perceive the ‘rising use of Bayesian methods in applied statistical work’ (p. 9), as supporting this Bayesian philosophy, the authors flatly declare that ‘most of the standard philosophy of Bayes iswrong’ (p. 10, n. 2). Despite their qualification that ‘A statisticalmethod can be useful even if its philosophical justification is in error’, their stance will rightly challenge many a Bayesian. This will be especially so when one has reached their third thesis, which seeks a new foundation that uses non-Bayesian ideas. Although the authors at first profess that their ‘perspective is not new’, but rather follows many other statisticians who emphasize ‘the value of Bayesian inference as an approach for obtaining statistical methods with good