[R] how calculation degrees freedom

[Peter Dalgaard]

Douglas Bates <dmbates at gmail.com> writes:


> > Of course, Monte Carlo p-values have their problems, but the world
> > is not perfect....
> 
> Another approach is to use mcmcsamp to derive a sample from the
> posterior distribution of the parameters using Markov Chain Monte
> Carlo sampling.  If you are interested in intervals rather than
> p-values the HPDinterval function from the coda package can create
> those.
> 

We (Søren and I) actually had a look at that, and it seems not to
solve the problem. Rather, mcmcsamp tends to reproduce the Wald style
inference (infinite DF) if you use a suitably vague prior.

It's a bit hard to understand clearly, but I think the crux is that
any Bayes inference only depends on data through the likelihood
function. The distribution of the likelihood never enters (the
hardcore Bayesian of course won't care). However, the nature of DF
corrections is that the LRT does not have its asymptotic distribution,
and mcmc has no way of picking that up.


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