alled so because it is irrelevant with data collection and model

ion. These a priori probabilities are assumed to exist before data

n as well as model construction.

ve interpretation of the a priori probabilities is the proportions of

ts belonging to two classes. Suppose the a priori probabilities of

ass problem are denoted by ߨ஺ and ߨ஻. If two classes have the

mber of data points, the simplest expression of two a priori

ties is an identical a priori probability, i.e., ߨ஺ൌߨ஻ൌ 0.5.

there are n data points for the class A and m data points for the

where ്݊݉. The simplest expressions of two a priori

ties are ߨ஺ൌ݊ሺ݊൅݉ሻ

⁄

and ߨ஻ൌ݉ሺ݊൅݉ሻ

⁄

for two classes,

ely. However, there are some slightly sophistic methods to

these a priori probabilities, such as the use of the Bayesian

approach. Two a priori probabilities must satisfy the following

s,

ߨ஺൅ߨ஻≡1

ߨ஺, ߨ஻൒0

(3.14)

e same time, a discriminant model is constructed based on a

data set. This process is named as an experiment, which has

o do with the a priori probabilities. In other words, the commonly

ximum likelihood process of model parameter optimisation of a

ation model will not utilise any knowledge from the a priori

ties. The two sets are independent from each other during a

process. Such an experimental outcome, i.e., a discrimination

s commonly called an empirical likelihood function or an

model because it is data-dependent.

d on two densities and two a priori probabilities and an empirical

he posterior probabilities (݌஺ and ݌஻) for two classes can be

A posterior probability model is a convolution between the a

obabilities and the likelihoods derived from an empirical model.

y, the posterior probabilities are derived in a post-experiment

Rather than defining an arbitrary threshold to make decisions or

likelihood function for decision making, using the posterior