[R-sig-ME] Uniform prior in mcmcsamp

[Ben Bolker]

On 04/12/2011 09:44 PM, Martin Krkosek wrote:
> Hi,
> 
> I am using the function pvals.fnc which uses mcmcsamp to extract HPD 
> credible intervals on a fixed effect in an lmer model. The only 
> information I can find on the prior distribution used on the fixed 
> effect is that it is "locally uniform".
> 
> How do I find out the interval of the uniform distribution that is 
> specified as the prior on the fixed effect?
> 
> Thank you
> 
> Martin
> 

  Martin,

  There is indeed not much information out there -- poking around in the
guts of the package I can't find much discussion, even in the draft
chapters of the book Doug Bates is writing.

  I believe that "locally uniform" here has a technical meaning --
rather than meaning it is necessary exactly uniform; for example, the
Jeffreys prior is (apparently) locally uniform.  I am still trying to
teach myself more about this -- my (old) copy of Bayesian Data Analysis
isn't helping very much.

<http://www.stats.org.uk/priors/Bayes6.pdf>
<http://www.statistik.lmu.de/institut/ag/biostat/teaching/lots2007/Hierarchical2-4.pdf>
(possibly? by Michael Höhle)

  The best I can do for myself at the moment is to poke through the code
in lmer.c:

  within mer_MCMCsamp, the standard deviation is being sampled from an
inverse-chi-squared distribution, scaled by the penalized weighted RSS;
  within MCMC_beta_u, the beta and u (random effect) values are sampled
from normal distributions;
  within MCMC_S, the theta_S (random effect variances etc.) are also
resampled from a normal distribution (probably on the log scale??)

  Sorry I can't be more helpful.

  Ben Bolker