show inference for pi in print.summary.varbvs

[timflutre]

As you say in your paper that the inference for pi is quite accurate (compare to full MCMC), I think it would be of interest to show it in the output of print.summary.varbvs. For that, if I'm not wrong, I think one could add the following commands, for instance just before the line "Selected variables by probability cutoff":

(pi.hat <- 10^(out$logodds$x0) / (1 + 10^(out$logodds$x0)))
(pi.hat.low <- 10^(out$logodds$a) / (1 + 10^(out$logodds$a)))
(pi.hat.high <- 10^(out$logodds$b) / (1 + 10^(out$logodds$b)))

and then:

cat("pi: ")
cat(sprintf("%0.3f [%0.3f,%0.3f]\n", pi.hat, pi.hat.low, pi.hat.high))

What do you think?

[pcarbo]

@timflutre It is accurate under the right circumstances---it is not always more accurate than MCMC.

Yes, I could add a line for pi, but I chose to show the prior log-odds instead that is the hyperparameter that is used in the model.

Do you think it would be confusing to show both logodds and pi?

[timflutre]

I tend to think that some users prefer pi and others logodds, hence both could be reported. To avoid confusion, you could simply add a sentence in the manual saying that one can be obtain from the other.

[pcarbo]

@timflutre I'm going to leave this open for now, but I have added a sentence about converting between the prior log-odds and the prior inclusion probability (see commit 022e0da). Part of the issue here is that I don't have a consistent notation for the prior inclusion probability (pi is awkward).

[timflutre]

@pcarbo ok, no problem, it's only a (very) small issue.