Is non-informative Bayesian analysis dangerous for wildlife???
Subhash Lele recently arXived a short paper entitled “Is non-informative Bayesian analysis appropriate for wildlife management: survival of San Joaquin Kit fox and declines in amphibian populations”. (Lele has been mentioned several times on this blog in connection with his data-cloning approach that mostly clones our own SAME algorithm.)
“The most commonly used non-informative priors are either the uniform priors or the priors with very large variances spreading the probability mass almost uniformly over the entire parameter space.”
The main goal of the paper is to warn, even better “to disabuse the ecologists of the notion that there is no difference between non-informative Bayesian inference and likelihood-based inference and that the philosophical underpinnings of statistical inference are irrelevant to practice.” The argument advanced by Lele is simply that two different parametrisations should lead to two compatible priors and that, if they do not not, this exhibits an unacceptable impact of the prior modelling on the resulting inference, while likelihood-based inference [obviously] does not depend on parametrisation.
The first example in the paper is a dynamic linear model of a fox population series when using a uniform U(0,1) prior on a parameter b against a Ga(100,100) prior on -a/b. (The normal prior a is the same on both.) I do not find the opposition between the two posteriors in the least surprising as the modelling starts by assuming different supports on the parameter b. And both are highly “informative” in that there is no intrinsic constraint on b that could justify the (0,1) support, as illustrated by the second choice when b is unconstrained, varying on (-15,15) or (-0.0015,0.0015) depending on how the Ga(100,100) prior is parametrised.
and the paper opposes a uniform prior on p,q to a normal N(0,10^3) prior on the logit transforms of p and q. [With an obvious typo at the top of page 10.] As shown on the above graph, the two priors on p are immensely different, so should lead to different posteriors in a weakly informative setting as a Bernoulli experiment. Even with a few hundred individuals. A somewhat funny aspect of this study is that Lele opposes the uniform prior to the Jeffreys Be(.5,.5) prior as being “nowhere close to looking like what one would consider a non-informative prior”, without noticing that the logit parametrisation normal prior leads to an even more peaked prior…
“Even when Jeffreys prior can be computed, it will be difficult to sell this prior as an objective prior to the jurors or the senators on the committee. The construction of Jeffreys and other objective priors for multi-parameter models poses substantial mathematical difficulties.”
I find it rather surprising that a paper can be dedicated to the comparison of two arbitrary prior distributions on two fairly simplistic models towards the global conclusion that “non-informative priors neither ‘let the data speak’ nor do they correspond (even roughly) to likelihood analysis.” In this regard, the earlier critical analysis of Seaman et al., to which my PhD student Kaniav Kamary and I replied, had a broader scope.