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existing among classes (in the hierarchical structure of classes, some classes can
share some model parameters). Detailed information about AutoClass can be
found in the Website http://ic-www.arc.nasa.gov/ic/projects/bayes-group/autoclass.
Above, we only list some typical applications of Bayesian method. The
applications of Bayesian method in data mining are far more to from these. The
Bayesian neural network, which combines Bayesian method and neural network,
and the Bayes Point Machine, which combines Bayesian method and statistical
learning, are all interesting examples of applications of Bayesian method.
Interested readers can find more in topic (Amari, 1985).
6.2 Foundation of Bayesian Probability
6.2.1
Foundation of probability theory
Probability is a branch of mathematics, which focuses on the regularity of
random phenomena. Random phenomena are phenomena that different results
appear under same conditions. Random phenomena include individual random
phenomena and substantive random phenomena. The regularity from the
observation of substantive random phenomena is called statistical regularity.
Statistically, we conventionally call an observation, a registration or an
experiment about phenomenon a trial. A random trial is an observation on a
random phenomenon. Under same condition, random trials may lead to different
results. But the sphere of all the possible results is estimable. The result of a
random trial is both uncertain and predictable. Statistically, the result of a
random trial is called random event, shortly by event.
Random event is the result that will appear or not appear in a random trial. In
random phenomenon, the frequency of a mark is the total number that the mark
appears in all trials.
Example 6.1
To study the product quality of a factory, we make some random
samplings. In each sampling, the number of samples is different. The result of
sampling is recoded and presented in Table 6.1.
Table 6.1 The result of sampling of product quality
Number of
products examined
5
10
50
100
300
600
1000
5000
10000
Number of
qualified products
5
8
44
91
272
542
899
4510
8999
Frequency of
qualification
1
0.8
0.88
0.91
0.907
0.892
0.899
0.902
0.8997
