Belief Models and Certainty Factors

This approach has been suggested by Shortliffe and Buchanan and used in their famous medical diagnosis MYCIN system.

MYCIN is essentially and expert system. Here we only concentrate on the probabilistic reasoning aspects of MYCIN.

• MYCIN represents knowledge as a set of rules.
• Associated with each rule is a certainty factor

• A certainty factor is based on measures of belief B and disbelief D of an hypothesis  given evidence E as follows:

where  is the standard probability.

• The certainty factor C of some hypothesis  given evidenceE is defined as: 
  

Reasoning with Certainty factors

• Rules expressed as if evidence list  then there is suggestive evidence with probability, p for symptom .
• MYCIN uses rules to reason backward to clinical data evidence from its goal of predicting a disease-causing organism.
• Certainty factors initially supplied by experts changed according to previous formulae.

• How do we perform reasoning when several rules are chained together?

Measures of belief and disbelief given several observations are calculated as follows:

• How about our belief about several hypotheses taken together? Measures of belief given several hypotheses and to be combined logically are calculated as follows:

Disbelief is calculated similarly.

Overcoming the Bayes Rule shortcomings

Certainty Factors do adhere to the rules of Bayesian statistics, but it can represent tractable knowledge systems:

• Individual rules contribute belief in an hypotheses -- basically a conditional probability.
• The formulae for combination of evidence / hypotheses basically assume that all rules are independent ruling out the need for joint probabilities.
• The burden of guaranteeing independence is placed on the rule writer.