Updating Probabilities: A Complex Agent Based Example

TL;DR

This paper demonstrates how the Maximum Entropy method can be applied to a complex, multi-agent system where agents with partial data and global constraints infer about the entire system, revealing emergent behaviors.

Contribution

It introduces a complex agent-based example of inference combining data and constraints, illustrating how local and global information sharing influences system behavior.

Findings

Agents can infer system properties using local data and global constraints.

Information sharing among agents affects emergent system behavior.

The method models systems with geometrical and local interaction structures.

Abstract

It has been shown that one can accommodate data (Bayes) and constraints (MaxEnt) in one method, the method of Maximum (relative) Entropy (ME) (Giffin 2007). In this paper we show a complex agent based example of inference with two different forms of information; moments and data. In this example, several agents each receive partial information about a system in the form of data. In addition, each agent agrees or is informed that there are certain global constraints on the system that are always true. The agents are then asked to make inferences about the entire system. The system becomes more complex as we add agents and allow them to share information. This system can have a geometrical form, such as a crystal structure. The shape may dictate how the agents are able to share information, such as sharing with nearest neighbors. This method can be used to model many systems where the agents or cells have local or partial information but must adhere to some global rules. This could also illustrate how the agents evolve and could illuminate emergent behavior of the system.