In this talk I discuss Statistical Filtering as an Informationally Dissipative System leading to a relation between Shannon Information and fisher Information. When viewed as a problem in Bayesian Inference the Optimal Fileter (Conditional Distribution ) corresponds to a variational Principle related to Free Energy Minimization. These ideas are related to the recent work of Otto, Jordan and Kinderlehrer on the variational Principle for the Fokker Planck Equation.
Information and Entry Flow in Statistical Filtering.
Sanjoy Mitter, MIT