Computation of Variances in Causal Networks

TL;DR

This paper introduces methods to compute variances in probabilities within causal networks, accounting for uncertainty in stored probabilities and inferred results, enhancing the interpretability of probabilistic inference.

Contribution

It presents algorithms for calculating prior variances of node probabilities and an approximation method for variances in inferred probabilities in causal networks.

Findings

Provides a method for determining prior variances of node probabilities.

Develops an approximation technique for variances in inferred probabilities.

Enhances probabilistic inference by quantifying uncertainty.

Abstract

The causal (belief) network is a well-known graphical structure for representing independencies in a joint probability distribution. The exact methods and the approximation methods, which perform probabilistic inference in causal networks, often treat the conditional probabilities which are stored in the network as certain values. However, if one takes either a subjectivistic or a limiting frequency approach to probability, one can never be certain of probability values. An algorithm for probabilistic inference should not only be capable of reporting the inferred probabilities; it should also be capable of reporting the uncertainty in these probabilities relative to the uncertainty in the probabilities which are stored in the network. In section 2 of this paper a method is given for determining the prior variances of the probabilities of all the nodes. Section 3 contains an approximation method for determining the variances in inferred probabilities.