Principle and Theory
In terms of classification, the Bayesian theorem allows us to combine prior
probabilities, along with observed evidence to arrive at the posterior probability. More
or less, conditional probabilities represent the probability of an event occurring given
evidence. According to the Bayesian Theorem, if
P(ω
i
)
,
P( X∨ω
i
)
,
i=1,2,3 , … c
, and X are known or given, the posterior probability can
be derived as follows
P
(
ω
i
|
X
)
=
P
(
X
|
ω
i
)
P(ω
i
)
∑
j=1
c
P
(
X
|
ω
i
)
P (ω
i
)
i=1,2,3 , … c
Let the series of decision actions as
{a
1
,a
2
, … a
c
}
, the conditional risk of
decision action a can be computed by
R
(
a
i
|
X
)
=
∑
j=1 , j ≠ i
c
λ
(
a
i
, ω
j
)
P
(
ω
j
)
i=1,2,3,…c
a
k
¿
= Arg min
i
R
(
a
i
|
X
)
i=1,2,3 , … c
