Toward a Market Model for Bayesian Inference

TL;DR

This paper introduces a novel market-based framework that maps Bayesian networks to economic models, enabling decentralized probabilistic inference and belief aggregation through market equilibrium prices.

Contribution

It presents a method to represent Bayesian networks within a general-equilibrium market model, linking probabilistic inference to economic equilibrium analysis.

Findings

Market equilibrium prices correspond to Bayesian network probabilities

Framework facilitates decentralized probabilistic inference

Potential applications in belief aggregation and resource allocation

Abstract

We present a methodology for representing probabilistic relationships in a general-equilibrium economic model. Specifically, we define a precise mapping from a Bayesian network with binary nodes to a market price system where consumers and producers trade in uncertain propositions. We demonstrate the correspondence between the equilibrium prices of goods in this economy and the probabilities represented by the Bayesian network. A computational market model such as this may provide a useful framework for investigations of belief aggregation, distributed probabilistic inference, resource allocation under uncertainty, and other problems of decentralized uncertainty.