Core Technologies for Developing Autonomous and Autonomic Systems - Autonomous and Autonomic Systems - page 100

constructed, even at the cost of more up-front effort, the resulting system
should be more robust. Serious consideration should be given to whether the
initial ease of fuzzy construction outweighs the robustness of more formal
modeling techniques.

5.3.2 Bayesian Reasoning

Bayesian reasoning is a family of techniques based on Bayesian statistics. Its
strength is the firm foundation of statistics on which it rests (hundreds of
years). It has a well-developed methodology for mapping real world problems
into statistical formulations, and if the causal model is accurate and the ev-
idence accurately represented, Bayesian systems give scientifically defensible
results.
In simple terms, Bayes' rule (or Bayes' theorem) states that the belief
one accords a hypothesis upon obtaining new evidence can be computed by
multiplying one's prior belief in the hypothesis and the likelihood that the
evidence would appear if the hypothesis were true. This rule can be used to
construct very powerful inferential systems.
Bayesian systems require causal models of the world. These models can be
developed by engineers using their knowledge of the system, or in some cases,
by analyzing empirical data. These models must be at the appropriate level
of detail for the system to make correct inferences. Multiple implementation
strategies have been developed to reason with Bayesian models once they
have been created. Figure 5.8 shows two methods for representing a Bayesian
model. Bayes nets encode the state information as nodes and causality as
links between the nodes. Figure 5.8 a shows a simple example. More recent
work has developed systems that can reason on the probabilistic equations
in a symbolical manner similar to Mathematica. An example data set can be
seen in Fig. 5.8 b .
Many implementations of Bayesian systems make a simplifying as-
sumption that the supplied evidence is completely independent from other

D

exp (A) = p (A)
exp (B) = p (B|A)
exp (C) = p (C|A)
exp (D) = p (D|BCF)
exp (E) = p (E)
exp (F) = p (F|E)

F B C

E A

(a) (b)

Fig. 5.8. Bayes network (a) and corresponding symbolic representation (b)