Toward a Market Model for Bayesian Inference
This provides a novel framework for belief aggregation and distributed inference in decentralized uncertainty problems, though it appears incremental as it builds on existing Bayesian and economic models.
The authors tackled the problem of representing probabilistic relationships in economic models by mapping a Bayesian network with binary nodes to a market price system, showing that equilibrium prices correspond to the network's probabilities.
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.