## 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.

Posted in Books, Statistics, University life with tags , , on October 16, 2012 by xi'an

Here is an email I got yesterday

Voila ma question: Comment programmer avec le Matlab la fonction de densité a posteriori (n’est pas de type connu qui égale au produit la fonction de vraisemblance et la densité de la loi a priori) pour calculer la valeur de cette fonction en un point theta=x (theta est le paramètre a estimer) en fixant les autres paramètres.

Here is my question: How to program with Matlab the posterior density function (which is not of a well-known type and which equals the product of the likelihood function by the prior density) for calculating the value of this function at a point theta = x (theta is the parameter estimate) while keeping the other parameters fixed.

which is a bit naïve, especially the Matlab part… I answered that the programming issue was kind of straightforward when the computation of both the prior density function and the likelihood function was feasible. (With Matlab or any other language.)

## computational difficulties [with notations]

Posted in R, Statistics, University life with tags , , , , on August 25, 2011 by xi'an

Here is an email I received from Umberto:

I have a doubt regarding the tempered transitions method you considered in your JASA article with Celeux and Hurn.

On page 961 you detail the several steps for building a proposal for a given distribution by simulating through l tempered power densities. I am slightly confused regarding the interpretation of your MCMC(x,π) notation.

For example does $MCMC(y_l,\pi^{1/\beta_{l-1}})$ means that an MCMC procedure starting at yl, say Metropolis-Hastings, is used to generate a single proposal yl+1 for $\pi^{1/\beta_{l-1}}$ ?

If this is the case, then yl+1 might be rejected or accepted and in the former case I would have yl+1=yl right? In other words I am not required to simulate proposals using $MCMC(y_l,\pi^{1/\beta_{l-1}})$ until I finally accept yl+1.

By reading the last paragraph in page 962 it seems to me that, indeed, the y1,…,y2l-1 thus generated are not necessarily accepted proposals for the corresponding power densities.

In retrospect, I still like this MCMC(x,π) notation in the simulated tempering “up-and-down” scheme (and the paper!). Because it is generic, in the sense of an R function that would take the function MCMC(x,π) as its input. To clarify the notation in this light, MCMC(x,π) returns a value that is the outcome of the corresponding MCMC step. This value may be equal to x (MCMC rejection) or to another value (MCMC acceptance). So the sequence y1,…,y2l-1 is made of consecutive values that differ and of consecutive values that do not (it is even possible that all the terms in the sequence are equal). At the end of this “up-and-down” tempering, the value y2l-1 may be the next value of the Markov chain targeted at the original target π. Or the current value may be replicated. This depends on the overall acceptance probability (4) on page 961. (Following Neal, 1996, Statistics and Computing.) This is a very compelling idea, whose mileage may vary depending on the number of required steps and powers.

The email address [xian@mylab.myuni.mycountry] is NOT unique.
the editorial staff for  further assistance