[R-sig-ME] pMCMC in languageR?

[David Duffy]

On Tue, 3 Jun 2008, Jonathan Baron wrote:

>            mcmc = mcmcsamp(object, n = nsim)
> #...
>            nr <- nrow(mcmc)
>            prop <- colSums(mcmc[, 1:ncoef] > 0)/nr
>            ans <- 2 * pmax(0.5/nr, pmin(prop, 1 - prop))
>
> This seems like a reasonable way to compute something like a p-value.
> It looks for the number of simulated cases on the wrong side of zero,
> and the "0.5/nr" is sort of like a minimum p-value to correct for the
> fact that the number of mcmc samples is finite.
>
> But it isn't a p-value of the usual sort.  It seems to be based on the
> posterior distribution of the parameters, given reasonable
> assumptions.

Some real Bayesians will hopefully pipe up, but are these posterior 
predictive P-values (Rubin 1984; Meng 1994) with H0: b=b_hat rather than 
b=0?  All the MCMC hypothesis testing/model discrepancy suggestions I know 
of seem to simulate replicates under a simpler null hypothesis and look 
for discrepancy with reality.  But if it is a single well-behaved 
parameter so that a Wald test is equivalent to a LRT, then isn't it merely 
the old question of which estimate of the variance to use (V|b0 or 
V|b_hat)?

-- 
| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v