݂ሺݔ௜ሻൌ෍ݓ௞࣮ሺݔ௜|ߙ௞, ߚ௞ሻ

௞ୀଵ

(2.14)

arameters of a Gamma mixture model can be estimated using the

d maximisation approach [Dempster, et al., 1977] or the Bayesian

[Mohammadi, et al., 2013] as well. mixR is an R package for

mma mixture modelling using the likelihood maximisation

. The function for estimating a Gamma mixture density in this

s mixfit. For instance, the following code was used to estimate

ty of the first replicate of the airway sequencing count data

et al., 2014] if the raw count data have been saved in a matrix x.

n-zero count data were logarithm transformed for the density

n. Figure 2.15(a) shows the estimated density, which shows a

mma mixture.

1+x)

umeric(x[which(x[,1]>0),1])

mixfit(z,ncomp=2,family='gamma')

(a) (b)

he Gamma mixture model for the first replicate of the airway sequencing count

he two component Gamma mixture model. Two thin curves stand for the

densities of two Gammas and the thick line stands for the final Gamma mixture

The model optimisation process based on the BIC in mixR.

mixR package also has a function for optimising the model

to select an optimal number of Gammas for a mixture based on

f the Bayesian Information Criterion (BIC) [Schwarz, 1978]. To