[R-sig-ME] Can an uninformative prior be too diffuse?

[Iain Stott]

Hi R-users

I'm having an interesting problem in using MCMCglmm for a meta analysis.

I run models as I would normally run them, with diffuse priors on
fixed and random effects (fixed: mu=0, V=10e8; random: V=1, nu=0.001;
gaussian model), and the posteriors I'm getting out of the models are
not like anything I've seen before. The range is very high but the
variance is very low, so that fixed effect posteriors are a spike
around the mean and random effects posteriors are highly truncated at
0. A handful of coefficient sets are taking extreme values that seem
to make no sense at all.

I wonder why this is: running for longer does not fix the problem and
the chains aren't autocorrelated. Parameter expansion does not help
the random coefficients. I'm always seeing a handful of samples that
are orders of magnitude larger than the data themselves (which are
real weighted mean differences over about -2 to 2) whilst the vast
majority are being taken from a much more sensible range.

It seems the only solution to getting better posteriors is to make
them less diffuse (decrease V for fixed effects, increase nu for
random effects). This makes sense, but I'm not comfortable doing it
when the posteriors are so sensitive to variances on the priors, and I
don't know what it would mean for interpretation of the model. I'm not
convinced that a prior can be "too" diffuse, and I'm not sure why
these extreme samples are being accepted. But then, perhaps allowing
the model to sample from a range that is so much larger than the data
just doesn't make sense... although like I say, I would have expected
these extreme values to be ditched based on likelihood.

If anyone can shed some light, it would be greatly appreciated. For
now I'll have to forego some of the random effects and forge ahead
with gls...


Iain

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Dr. Iain Stott
Environment and Sustainability Institute
University of Exeter, Cornwall Campus
Tremough, Treliever Road
Penryn, Cornwall, TR10 9FE, UK.
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http://www.exeter.ac.uk/esi/
http://biosciences.exeter.ac.uk/cec/