Noninformative prior for GP mean

[John McFarland]

I was just doing some quick testing of fitting GP models with MCMC and
am seeing some strange behavior when I try to approximate a
noninformative prior with a Normal distribution having a very large
variance. I'm still learning pymc, so there's a good chance I'm doing
something wrong.

Basically I'm just fitting a GP model to some data, and I'm modeling the
GP as having a constant but unknown mean (call it beta). The data were
generated from a GP with 0 mean. When I use the Uninformative prior
distribution object, I get the expected results: the marginal posterior
for beta is pretty much centered at 0 and shows support over about -2,2.
Just to try and understand how some of the other pymc distribution
objects worked, I also tried approximating a non-informative prior with
Normal(0, 0.00001) -- this should be a flat prior so I would expect it
to be a reasonable approximation to a constant prior. However, with
this prior, the marginal posterior for beta is much different, showing
support over roughly -2000,2000.

Am I missing something?

I'm attaching the code and small data file.

Thanks,
John

[Anand Patil]

Hi John,

Thanks for the report. This isn't a GP-specific problem. The proximal cause is that GPSampler was mistakenly taking beta as dataless when assigning step methods, meaning it can be safely sampled from its conditional prior.

Issue http://code.google.com/p/pymc/issues/list?thanks=346&ts=1294660820 traces through to the original bug, which is a pretty nasty one. We'll get it fixed ASAP.

Anand

-2.000000 -0.416758
-1.428571 -1.562763
-0.857143 -2.934006
-0.285714 -2.772527
0.285714 -1.255265
0.857143 0.437696
1.428571 0.410467
2.000000 -0.056267

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