13.3 Intensional Approaches to Uncertainty 329
variables satisfy various simplifying properties. The most common simplifi-
cation is to assume that the random variables are statistically independent.
This assumption works well for many random processes, such as card games
and queues, but it does not capture the more complex processes that occur
in biological systems, where interdependence is very common.
Another disadvantage of probability theory is that probabilistic inference
is not the result of a propagation process as it is for the extensional ap-
proaches. This makes the intensional approach incompatible with rule-based
reasoning systems.
Thus in spite of the advantages of probability theory pragmatically and
theoretically, other approaches to uncertainty have been introduced that are
more computationally tractable and more compatible with logical reasoning
systems. However, new techniques and algorithms for probabilistic reason-
ing have now been introduced that have made it much more tractable as well
as more compatible with rule-based systems. These techniques are discussed
in chapter 14.
Summary
- Probability theory is the dominant intensional approach to uncertainty.
- Probabilistic statements are called events.
- A random variable is a collection of events distinguished from one an-
other by a value of the variable. - A stochastic model is a set of random variables together with their joint
probability distribution. - Conditional probability is the most basic from of inference in probability
theory. - Bayes’ Law is the basis for diagnostic inference and subjective probabili-
ties. - The Dutch book argument shows that Bayesian analysis is always better
than non-Bayesian analysis. - Probability theory has long been regarded as being too computationally
complex to be the basis for modeling the uncertainty of large systems, but
new techniques have been introduced that are changing this.