The Bounded Bayesian

TL;DR

This paper develops a theoretical framework for how bounded Bayesian agents manage and revise simplified models, analyzing their convergence to ideal Bayesian reasoning in probability forecasting tasks.

Contribution

It introduces a formal approach to understanding model management in fallibly rational agents and provides conditions for convergence to larger-world probabilities.

Findings

Conditions for convergence of small-world models to larger-world probabilities

Analysis of search processes over small models as approximations

Framework for managing and revising models in bounded rationality

Abstract

The ideal Bayesian agent reasons from a global probability model, but real agents are restricted to simplified models which they know to be adequate only in restricted circumstances. Very little formal theory has been developed to help fallibly rational agents manage the process of constructing and revising small world models. The goal of this paper is to present a theoretical framework for analyzing model management approaches. For a probability forecasting problem, a search process over small world models is analyzed as an approximation to a larger-world model which the agent cannot explicitly enumerate or compute. Conditions are given under which the sequence of small-world models converges to the larger-world probabilities.