METASYSTEMS AND THE MAXIMUM ENTROPY PRINCIPLE

Abstract

A probabilistic model of data that is an extension of the standard relational model predominant in database management applications is introduced in [Cavallo and Pittarelli. 1987] and elaborated in [Pittarelli, 1993 and 1994]. A probabilistic database instance is identical to what, in the GSPS hierarchy of systems types [Klir, 1985], is referred to as a probabilistic structure behavior system.

We discuss the problem of modifying a probabilistic structure system to accommodate new information. This corresponds to what, in the literature on databases, is referred to as an update. A sequence of probabilistic structure systems, each the result of modifying its predecessor, may be regarded as a metasystem [Klir, 1985]. We will focus on computational aspects of replacing one structure system with its successor. A distinction is made between global and local updating of a structure system, using Bayesian or quasi-Bayesian methods. A global update consists of selecting an element of the reconstruction family, updating it appropriately, then projecting. A local update propagates the effect of updating a single behavior function to the other elements of the structure system. It is shown that Bayesian local updating produces the same structure system that results when the maximum entropy element of the reconstruction family is selected as the basis for a Bayesian global update.

INDEX TERMS:

• Maximum entropy
• information theory
• metasystems
• databases