I increased the range of the plot from Statistics is easy! part 2 and added the 2.5% and 97.5% percentiles from a WinBugs run on the same problem … using bugs() of course

And then started to worry about that nasty bump on the right of the 97.5% percentiles

Did not take long to realize the default numerical integration was failing – too bad it did so – so smoothly.

Located a program I wrote a couple years ago to do _guaranteed_ upper and lower bounds for integrals based on envelope rules by Evans and Swartz – too bad I did not write comments in it.

But I did confirm the above is very close at log odds of 2 and definitely too high at log odds of 6. With some more careful programing I soon should be able to get upper and lower curves that bound where the integrated log likelihood should be!

But it does seem like a lot of work to make such a simple problem look easy.

But then, it would by a _fail safe_ diagnostic for MCMC convergence

for problems involving just 2 parameters

( and the guarantee and fail safe do depend on some contions )

Maybe statistics was not meant to be made to look easy.

K?