Bayesian Analysis in Expert Systems

TLDR

The paper reviews recent developments in applying Bayesian probabilistic and statistical ideas to expert systems. The authors illustrate how Bayesian ideas are implemented in expert systems by representing knowledge in belief networks, performing exact inference via propagation, updating priors with data using Dirichlet distributions, and transforming the model into a junction tree for efficient computation. They show that Bayesian statistical techniques can update subjective inputs and provide diagnostics to detect conflicts between data and prior specifications.

Abstract

We review recent developments in applying Bayesian probabilistic and statistical ideas to expert systems. Using a real, moderately complex, medical example we illustrate how qualitative and quantitative knowledge can be represented within a directed graphical model, generally known as a belief network in this context. Exact probabilistic inference on individual cases is possible using a general propagation procedure. When data on a series of cases are available, Bayesian statistical techniques can be used for updating the original subjective quantitative inputs, and we present a set of diagnostics for identifying conflicts between the data and the prior specification. A model comparison procedure is explored, and a number of links made with mainstream statistical methods. Details are given on the use of Dirichlet prior distributions for learning about parameters and the process of transforming the original graphical model to a junction tree as the basis for efficient computation.