Conditional event algebra techniques for iterated image estimation

Abstract

Practical sequential estimation algorithms inherently involve "iterated conditioning"; that is, the estimate at any algorithm step is conditioned o n information passed f r o m the previous step. Except in special cases, standard probability theory cannot deal with operations like iterated conditioning, so it is dificult even to formulate algorithms that make optimal use of the available information. The recently developed Product Space Conditional Event Algebra (PS-CEA) allows f o r the definition of '%onditional events" as regular events in a probability space, and thus f o r the extension of Bayesian analysis to cases of iterated conditioning. I n this paper, we describe the P S -C E A approach and give a n example of its use in deriving iterated image estimators when the information passed f r o m one stage to the next is the current image estimate.