Updating Probabilities: A Complex Agent Based Example
Univerisity at Albany
Last modified: March 26, 2008
It has been shown that one can accommodate both data (Bayes) and constraints (MaxEnt) in one method, the method of Maximum (relative) Entropy (ME) (Giffin 2007). This method can process these forms of information simultaneously thus ensuring that the constraints always hold, unlike what has been traditionally done.
The main result of this paper is to show a specific and detailed complex agent based example of inference with two different forms of information; moments and observable data by way of the ME method. 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 point of this example is to show how different agents predict different outcomes following the above model. The system becomes more complex as we add agents and allow them to share information. This system can have geometrical forms, such as a crystal structure. The shape may dictate how the agents are able to share information, such as sharing with nearest neighbors.
This model of inference may help solve problems in a wide variety of fields such as ecology, economics, physics and machine learning. Any system where the agents or cells have local or partial information but must adhere to some global rules can be modeled with this method.