I am happy that you mention Gelman’s book (I am studying it right now). I think lots of “naive strong bayesianists” would improve from a thoughtful study of the BDA book (there are lots of worked out demos and exercises available for it) and maybe some practical application of Bayesian modelling to some real-world statistical problems. The practice of “Bayesian way of life” of “updating my priors” sounds always a bit too easy in contrast to doing a genuine statistical inference.
For example, a couple of puzzles I am still myself unsure how to answer properly and with full confidence: Why one would be interested in doing stratified random sampling with your epidemiological study instead of naive “collect every data point that you see and then do a Bayesian update?” Or how multiple comparisons corrections for classical frequentist p-values map into Bayesian statistical framework? Does it matter for LWian Bayesianism if you are doing your practical statistical analyses with frequentist or Bayesian analysis tools (especially if many frequentist methods can be seen as clever approximations to full Bayesian model, see e.g. discussion of Kneser-Ney smoothing as ad hoc Pitman-Yor process inference here: https://cs.stanford.edu/~jsteinhardt/stats-essay.pdf ; similar relationship exists between k-means and EM-algorithm of Gaussian mixture model.) And if there is no difference, is the philosophical Bayesianism then actually that important—or important at all—for rationality?
I am happy that you mention Gelman’s book (I am studying it right now). I think lots of “naive strong bayesianists” would improve from a thoughtful study of the BDA book (there are lots of worked out demos and exercises available for it) and maybe some practical application of Bayesian modelling to some real-world statistical problems. The practice of “Bayesian way of life” of “updating my priors” sounds always a bit too easy in contrast to doing a genuine statistical inference.
For example, a couple of puzzles I am still myself unsure how to answer properly and with full confidence: Why one would be interested in doing stratified random sampling with your epidemiological study instead of naive “collect every data point that you see and then do a Bayesian update?” Or how multiple comparisons corrections for classical frequentist p-values map into Bayesian statistical framework? Does it matter for LWian Bayesianism if you are doing your practical statistical analyses with frequentist or Bayesian analysis tools (especially if many frequentist methods can be seen as clever approximations to full Bayesian model, see e.g. discussion of Kneser-Ney smoothing as ad hoc Pitman-Yor process inference here: https://cs.stanford.edu/~jsteinhardt/stats-essay.pdf ; similar relationship exists between k-means and EM-algorithm of Gaussian mixture model.) And if there is no difference, is the philosophical Bayesianism then actually that important—or important at all—for rationality?