The demo of DSG. The solid line stands for the null density ݂଴. The dotted line

he alternative density ݂ଵ. The pair of the filled dots stands for a non-DEG. The

riangles stands for a DEG.

ndard DSG density function ݂ሺܢ|ߠሻ given the model parameters

ߤଵ, ߪ଴

ଶ, ߪଵ

ଶ, ݓ଴, ݓଵሽ has the form shown below,

݂ሺܢ|ߠሻ ൌݓ଴࣡ሺܢ|ߤ଴, ߪ଴

ଶሻ൅ݓଵ࣡ሺܢ|ߤଵ, ߪଵ

ଶሻ

(6.43)

൏ݓ௠൏1 is the mixing coefficient or weight of the m^th Gaussian

ݓଵൌ1

࣡ሺܢ|ߤ௠, ߪ௠^ଶሻൌ

1

ඥ2ߨߪ௠^{ଶexp ቆെ}

ሺܢെߤ௠ሻ^ଶ

2ߪ௠^ଶ

ቇ

(6.44)

ch a model, ߪ଴

ଶ is the variance of the null density and ߪଵ

ଶ≫ߪ଴

ଶ is

nce of the alternative density. When this condition is satisfied, it

en that the alternative density will be much more flattened. This

also called a two-component Gaussian mixture model. In this

ሺܢ|ߤ଴, ߪ଴

ଶmodels the uninformative subset of the data. In this

ሻ

e data has a little variation from zero, hence uninformative. Most

Gs will belong to this category, hence the null data. The other

nt ࣡ሺܢ|ߤଵ, ߪଵ

ଶሻ models the informative subset of the data. The

ts (genes) in this subset have a great deviation from zero. Most

ill have a great scale of the deviation from zero, hence very

ve. A small ߪ଴

ଶ naturally leads to a sharp peak centred at ߤ଴.

≫ߪ଴

ଶ, ࣡ሺܢ|ߤଵ, ߪଵ

ଶሻ approximates a uniform distribution in the

case and the identification of the null data is straightforward. The

d function of such a model is defined as below,