## Bayesian multimodel inference by RJMCMC: A Gibbs sampling approach

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , on December 27, 2013 by xi'an

Barker (from the lovely city of Dunedin) and Link published a paper in the American Statistician last September that I missed, as I missed their earlier email about the paper since it arrived The Day After… The paper is about a new specification of RJMCMC, almost twenty years after Peter Green’s (1995) introduction of the method. The authors use the notion of a palette, “from which all model specific parameters can be calculated” (in a deterministic way). One can see the palette ψ as an intermediary step in the move between two models. This reduces the number of bijections, if not the construction of the dreaded Jacobians!, but forces the construction of pseudo-priors on the unessential parts of ψ for every model. Because the dimension of ψ is fixed, a Gibbs sampling interleaving model index and palette value is then implementable. The conditional of the model index given the palette is available provided there are not too many models under competitions, with the probabilities recyclable towards a Rao-Blackwell approximation of the model probability. I wonder at whether or not another Rao-Blackwellisation is possible, namely to draw from all the simulated palettes a sample for the parameter of an arbitrarily chosen model.

## 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.

## Model weights for model choice

Posted in Books, R, Statistics with tags , , , , , , on February 10, 2011 by xi'an

An ‘Og reader. Emmanuel Charpentier, sent me the following email about model choice:

I read with great interest your critique of Peter Congdon’s 2006 paper (CSDA, 50(2):346-357) proposing a method of estimation of posterior model probabilities based on improper distributions for parameters not present in the model inder examination, as well as a more general critique in your recent review of M. Aitkin’s recent book.

However, Peter Congdon’s 2007 proposal (Statistical Methodology. 4(2):143-157.) of another method for model weighting seems to have flown under your radar ; more generally, while the 2006 proposal seems to have been somewhat quoted and used in at least one biological application and two financial applications, ihis 2007 proposal seems to have been largely ignored (as far as a naïve Google Scholar’s user can tell) ; I found no allusion to this technique neither in your blog nor on Andrew Gelman’s blog.

This proposal, which uses a full probability model with proper priors and pseudo-priors, seems, however, to answer your critiques, and offers a number of technical advantages over other proposal :

1. it can be computed from separate MCMC samples, with no regard to the MCMC sapling technique used to obtain them, therefore allowing the use of the « canned expertise » existing in WinBUGS, OpenBUGS or JAGS (which entails the impossibility of controlling the exact sampling methods used to solve a given problem) ;
2. it avoids the needs of very long runs to sufficiently explore unlikely models (which is the curse of Carlin & Chib (1995) method) ;
3. it seems relatively easy to compute in most situations.

I’d be quite interested by any writings, thoughts or reactions to this proposal.

As I had indeed missed this paper, I went and took a look at it.