Update of Prior Probabilities by Minimal Divergence

Abstract

The present paper investigates the update of an empirical probability distribution with the results of a new set of observations. The update reproduces the new observations and interpolates using prior information. The optimal update is obtained by minimizing either the Hellinger distance or the quadratic Bregman divergence. The results obtained by the two methods differ. Updates with information about conditional probabilities are considered as well.

Keywords

• statistical update procedure
• minimal divergence
• Hellinger distance
• Bregman divergence
• Jeffrey conditioning