A discussion on Bayesian analysis : Selecting Noninformative Priors

Following an earlier post on the American Statistician 2013 paper by Seaman III and co-authors, Hidden dangers of specifying noninformative priors, my PhD student Kaniav Kamary wrote a paper re-analysing the examples processed by those authors and concluding to the stability of the posterior distributions of the parameters and to the effect of the noninformative prior being essentially negligible. (This is the very first paper quoting verbatim from the ‘Og!) Kaniav logically submitted the paper to the American Statistician.

hidden dangers of noninformative priors

Last year, John Seaman (III), John Seaman (Jr.), and James Stamey published a paper in The American Statistician with the title Hidden dangers of specifying noninformative priors. (It does not seem to be freely available on-line.) I gave it to read to my PhD students, meaning to read towards the goal of writing a critical reply to the authors. In the meanwhile, here are my own two-cents on the paper.

“Applications typically employ Markov chain Monte Carlo (MCMC) methods to obtain posterior features, resulting in the need for proper priors, even when the modeler prefers that priors be relatively noninformative.” (p.77)

Apart from the above quote, which confuses proper priors with proper posteriors (maybe as the result of a contagious BUGS!), and which is used to focus solely and sort-of inappropriately on proper priors, there is no hard fact to bite in, but rather a collection of soft decisions and options that end up weakly supporting the authors’ thesis. (Obviously, following an earlier post, there is no such thing as a “noninformative” prior.) The paper is centred on four examples where a particular choice of (“noninformative”) prior leads to peaked or informative priors on some transform(s) of the parameters. Note that there is no definition provided for informative, non-informative, diffuse priors, except those found in BUGS with “extremely large variance” (p.77). (The quote below seems to settle on a uniform prior if one understands the “likely” as evaluated through the posterior density.) The argument of the authors is that “if parameters with diffuse proper priors are subsequently transformed, the resulting induced priors can, of course, be far from diffuse, possibly resulting in unintended influence on the posterior of the transformed parameters” (p.77).