Fig. 3.9. The logistic function with different parameter values.

asic component of the Bernoulli function is called the binary

MacKay, 2003], i.e., ߴൌ݌^௬ሺ1 െ݌ሻ^ଵି௬, where ݕ∈ሼ0,1ሽ and

. When y = 1 and p = 1.0 or y = 0 and p = 0.0, ߴ is maximised.

ameters ߙ and ߚ can be estimated through maximising this

d function. The logistic regression algorithm has been applied for

g interaction prediction [Celebi, et al., 2019] and common cancer

[Lopes, et al., 2019]. The R function for constructing a logistic

n analysis model is glm. 

e Bayesian linear discriminant analysis

o deliver a more robust discriminant analysis model, the Bayesian

has been introduced for linear discriminant analysis as well. In a

learning discriminant analysis model, the a priori probabilities

onger simply the proportions of data points belonging to two

nstead, they are parameters to be estimated using the a priori

[Zhou, et al., 2013]. Suppose the likelihood function of the model

rs is defined as below,

݌ሺܡ|ܟ, ߚሻൌ൬^ߚ

2ߨ^൰

ே/ଶ

exp ൬െ^ߚ

2 ^{|܆௧ܟെܡ|ଶ൰}

(3.23)

priori function of model parameters is defined as below,

݌ሺܟ|ߙሻൌቀ^ߙ

2ߨ^ቁ

ௗ/ଶ

exp ቀെ^ߙ

2 ^ܟ௧ܟቁ

(3.24)

se of the maximum a posterior probability approach leads to a

be formulated as below,