Page 305 - Contributed Paper Session (CPS) - Volume 4

CPS2233 Sharon Lee
Where and are independent random effects (RE) terms that govern

the scaling and translation of µ from µ , respectively. These RE terms are

independently distributed as
~ (1 , )

and
~(0, )

Where = 1 and 1 , is a -dimensional vector with all elements being

one. It follows that the batch template has a mixture of MST distributions with
component distributions given by

(µ , , , ) for = 1, … , . This template is useful not only as a

representative summary of the batch that facilitates visualization, but can be a
powerful tool in downstream analyses such as across-batch comparisons and
new sample classification. The latter can assist in clinical diagnosis of diseases.

Fitting the Hcyto model
The expectation-maximization (EM) algorithm (Dempster et al., 1977) has
become a standard tool for carrying out maximum likelihood estimation of the
parameters of finite mixture models. As both the lower- and upper- levels of
Hcyto can be written as a mixture model, these models can be fitted via the
EM algorithm. The technical details are omitted due to length restrictions, but
the procedure for the lower-level models are similar to that for the MST
mixture model by Pyne et al. (2009). They can be expressed in a hierarchical
form involving a normal, a gamma, and a half normal random variable. With
the upper-level, a further layer is added to this hierarchical form, leading to
|µ , , , ~ (µ + | |, )

µ | ~ (µ , + )

| , ~(0,1)

| ~( , )
2 2
~ ( )

where is the diagonal matrix with diagonal elements given by µ , is the

diagonal matrix given by , denotes the (univariate) half-normal

distribution, Gamma(·) denotes the gamma distribution, and ( )

denotes the multinomial distribution with categories and probabilities

= ( 1 , 2 , … , ) . Note that although the Hcyto model consists of
two levels, the model fitting procedure simultaneously estimate all parameters
of the model (that is, including both the lower and upper levels) in a single
step. No pre-processing or post-hoc steps are required.

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