Kai Puolamäki, Jarkko Salojärvi, Eerika Savia and Samuel Kaski
In: The Learning Workshop, 04 Apr - 07 Apr 2006, Snowbird, Utah, USA.
We discuss Bayesian modeling in the case where the model is
incorrect. Standard posterior distribution is optimal for
inference if the true model is within the model family. In the
case of an incorrect model, we show that for inference on
conditioned distribution, a different posterior-type
distribution is optimal. We provide here an axiomatic justification of
previously suggested supervised posterior distribution, introduce
Markov Chain Monte Carlo -type methods for computing with the
posterior, and demonstrate empirically that it works as expected.