gene. However the bimodal index value returned by the BI test

, which was greater than the threshold (1.06) determined by a

g process. Therefore the BI test classified this gene as a bimodal

was therefore untrue.

-scale Gaussian model for small replicate data DEG discovery

al data often has a problem of having insufficient replicates,

uses the difficulty of robust DEG discovery. This section will

an alternative called the dual-scale Gaussian model (DSG)

n model a gene expression data set without replicate or with a few

s [Everson, 2014; Al watban, 2015].

e dual-scale Gaussian model

he working principle of DSG

mixture model composed of two Gaussian components with an

centre for both Gaussian components but different variances as

Figure 6.47 [Bertschinger, 2001; Billings, et al., 2007; Kramer,

07]. A vector ܢൌሼݖ௜ሽ௜ୀଵ

௡ is assumed to follow a mixture of two

s. One of them has a smaller variance which is referred to as the

sity ݂଴ and the other has a greater variance referred to as the

e density ݂ଵ. Figure 6.47 demonstrates the working principle of

e null density ݂଴ has a smaller variance, hence a sharp peak at the

ro. The alternative density ݂ଵ has a greater variance, hence a

curve extending towards two extremes. The identification of a

ends on the magnitudes of ݂଴ and ݂ଵ. For instance, a gene marked

ir of the dots in the figure is identified as a non-DEG because of

onship ݂଴൐݂ଵ. However, a gene marked by the pair of the

is identified as a DEG because of the relationship ݂଴൏݂ଵ.