0). These delta expressions are saved in a variable named as ∆

low,

∆ൌሺߜଵ, ߜଶ, ⋯, ߜெሻ

(6.41)

ൌܰൈሺܭെ1ሻ is the number of all the delta expressions for a

with N genes and K replicates. Note that all the entries of ∆ should

ve. However, in case there might be some identical expressions

me genes, zero delta expressions may occur and are removed

f they present before proceeding to the following stages. It is

that ∆ follows a Gamma distribution which is shown below,

∆~ܩሺߜ|ߙ, ߚሻൌ^{ߚఈߜఈିଵ݁ିఉఋ}

Γሺߙሻ

(6.42)

two parameters ߙ and ߚ have been estimated, the Gamma

unction is then used for evaluating the gene-wise delta expression

nce, i.e., to calculate a p value for each delta expression of each

ene expressions of real data often contain outliers. It is therefore

to distinguish between outliers and bimodality. If there are one or

licates far away from the main expression cluster for a gene, these

should be treated as the outliers. This is because they can hardly

subpopulation for the further meaningful biomedicine

tion. In other words, such a phenomenon does not lead to the

on of a bimodal gene. Any outlier if it has been discovered, will

ved. Afterwards, whether there is more significant delta

n is examined again for the gene. If so, the gene is treated as a

dal gene or a bimodal gene.

e 6.37 shows an example. In this example, there are two replicates

emely low expressions. The second delta expression between the

nd the third replicates from the bottom upwards is significant.

, these two replicates (triangles) with the extremely low

ns should not be considered as one of two clusters of a bimodal

ause of too few replicates for forming a subpopulation with a

ine significance. Removing these two outliers, another