## Transferring Prior Information Between Models
Using Imaginary Data

**Radford M. Neal,
Dept. of Statistics and Dept. of Computer Science, University of Toronto**

Bayesian modeling is limited by our
ability to formulate prior distributions that adequately represent our
actual prior beliefs - a task that is especially difficult for
realistic models with many interacting parameters. I show here how a
prior distribution formulated for a simpler, more easily understood
model can be used to modify the prior distribution of a more complex
model. This is done by generating imaginary data from the simpler
``donor'' model, which is conditioned on in the more complex
``recipient'' model, effectively transferring the donor model's
well-specified prior information to the recipient model. Such prior
information transfers are also useful when comparing two complex
models for the same data. Bayesian model comparison based on the
Bayes factor is very sensitive to the prior distributions for each
model's parameters, with the result that the wrong model may be
favoured simply because the prior for the right model was not
carefully formulated. This problem can be alleviated by modifying
each model's prior to potentially incorporate prior information
transferred from the other model. I discuss how these techniques can
be implemented by simple Monte Carlo and by Markov chain Monte Carlo
with annealed importance sampling. Demonstrations on models for
two-way contingency tables and on graphical models for categorical
data show that prior information transfer can indeed overcome
deficiencies in prior specification for complex models.

Technical Report No. 0108, Dept. of Statistics, University of Toronto
(July 2001), 29 pages:
postscript,
pdf,
associated software.

(By mistake, this tech report was briefly released with the number 0107.
The content of that version was identical to this version.)

The results in this paper were produced using software available on-line.

Note: I have since learned of similar work that goes under the
name of "expected-posterior prior distributions".