Message
Hi
All,
I have been trying
different model selections methods and
have a question
about Newton/Raftery method for computing the marginal distribution of the
data:
P(Data) = [ int
P(Data| Parameters)^{-1} dP(Parameters|Data) ]^{-1}.
The situation I am
looking at is conjugate, normal-inverted gamma regression where
P(Data) is
known to be a t-distribution.
The NR approximation
usually indicates the correct model, but it consistently over-estimates the
known P(Data),
regardless of the
sample size, number of MCMC iterations, & prior parameters.
My null hypothesis
is that I have a bug, but other approximations, such as
int
P(Data|Parameter)*dP(Parameter), Gelfand & Dey, Chib & Carlin, and
reversible jump, get very close to P(Data).
The literature on NR
states the method is consistent in the number of MCMC
iterations.
In this example, the
NR approximation stabilizes at the wrong value as a function of iterations (I
only went out 100K).
Any
insights?
Thanks
Peter
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