The Role of Information Geometry in Updating States of Knowledge

David J. Blower

Abstract

Information Processors routinely update their state of knowledge about the world they inhabit. How do they (and we as well) go about accomplishing this in an optimal fashion? I present an overview of a probabilistic approach to how Information Processors predict what will happen next given measurements of relevant variables and knowing what has happened in the past.

Part of the answer to this kind of updating takes place at a purely formal level where abstract probability symbols are manipulated according to known theorems. The more interesting half of the updating problem involves justifying a numerical assignment to the abstract probability symbols. This is where Information Geometry plays a distinctive and vital role. Information Geometry explains and inspires models that incorporate information about the relationship between what needs to be updated and what this critical event might depend on.

 

I will discuss some of the technical aspects involved in generating models through the auspices of Information Geometry. The essential core concepts can be communicated by a couple of easy numerical examples. After this much has been absorbed, the path to more complicated problems lies relatively unobstructed.