## hidden dangers of noninformative priors

Posted in Books, Statistics, University life with tags , , , , , on November 21, 2013 by xi'an

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).

## can you help?

Posted in Statistics, University life with tags , , , , , , , on October 12, 2013 by xi'an

An email received a few days ago:

I want to compare the predictive power of a non Bayesian model (GWR, Geographically weighted regression) and a Bayesian hierarchical model (spLM).
For GWR, DIC is not defined, but AIC is.
For  spLM, AIC is not defined, but DIC is.

How can I compare the predictive ability of these two models? Does it make sense to compare AIC of one with DIC of the other?

I did not reply as the answer is in the question: the numerical values of AIC and DIC do not compare. And since one estimation is Bayesian while the other is not, I do not think the predictive abilities can be compared. This is not even mentioning my reluctance to use DIC…as renewed in yesterday’s post.

## seminar at CREST on predictive estimation

Posted in pictures, Statistics, University life with tags , , , , , , , , on March 6, 2012 by xi'an

On Thursday, March 08, Éric Marchand (from Université de Sherbrooke, Québec, where I first heard of MCMC!, and currently visiting Université de Montpellier 2) will give a seminar at CREST. It is scheduled at 2pm in ENSAE (ask the front desk for the room!) and is related to a recent EJS paper with Dominique Fourdrinier, Ali Righi, and Bill Strawderman: here is the abstract from the paper (sorry, the pictures from Roma are completely unrelated, but I could not resist!):

We consider the problem of predictive density estimation for normal models under Kullback-Leibler loss (KL loss) when the parameter space is constrained to a convex set. More particularly, we assume that

$X \sim \mathcal{N}_p(\mu,v_x\mathbf{I})$

is observed and that we wish to estimate the density of

$Y \sim \mathcal{N}_p(\mu,v_y\mathbf{I})$

under KL loss when μ is restricted to the convex set C⊂ℝp. We show that the best unrestricted invariant predictive density estimator p̂U is dominated by the Bayes estimator p̂πC associated to the uniform prior πC on C. We also study so called plug-in estimators, giving conditions under which domination of one estimator of the mean vector μ over another under the usual quadratic loss, translates into a domination result for certain corresponding plug-in density estimators under KL loss. Risk comparisons and domination results are also made for comparisons of plug-in estimators and Bayes predictive density estimators. Additionally, minimaxity and domination results are given for the cases where: (i) C is a cone, and (ii) C is a ball.