Transferring Prior Information Between Models Using Imaginary Data
Bayesian modeling is limited by our ability to formulate prior distributions that adequately represent our actual prior beliefs | a task that is especially diicult 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, eeectively transferring the donor model's well-speciied 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 deeciencies in prior speciication for complex models.