An Implementation of a Method for Computing the Uncertainty in Inferred Probabilities in Belief Networks

TL;DR

This paper presents two methods for quantifying the uncertainty in inferred probabilities within belief networks, addressing a gap in existing probabilistic inference algorithms by providing error estimates.

Contribution

It introduces and compares the Approximate Propagation and Monte Carlo Integration methods for computing variance in belief network inferences, enhancing decision-making reliability.

Findings

Both methods effectively estimate uncertainty in inferred probabilities.

The Approximate Propagation method is faster but less accurate than Monte Carlo.

Monte Carlo provides more precise uncertainty estimates at higher computational cost.

Abstract

In recent years the belief network has been used increasingly to model systems in Al that must perform uncertain inference. The development of efficient algorithms for probabilistic inference in belief networks has been a focus of much research in AI. Efficient algorithms for certain classes of belief networks have been developed, but the problem of reporting the uncertainty in inferred probabilities has received little attention. A system should not only be capable of reporting the values of inferred probabilities and/or the favorable choices of a decision; it should report the range of possible error in the inferred probabilities and/or choices. Two methods have been developed and implemented for determining the variance in inferred probabilities in belief networks. These methods, the Approximate Propagation Method and the Monte Carlo Integration Method are discussed and compared in this paper.