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CPS1954 Vincent C. et al.
obtained directly from the regression coefficients because represents the

rate of change in the HAZ between years and +1 .

So far, we have not mentioned any distributional assumption on the
growth velocity vector = ( , . . . ) . Anderson et al. (2018) and Lee et

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al. (2018) model as realisations from a multivariate ( , Σ ) distribution

with mean vector and covariance matrix Σ . This signifies a homogeneous

population model where individual growth profiles largely follow the trend of
a global trajectory and the variability of deviation from this mean curve is
determined by Σ . On average, the rate of growth is the same for all children

in the population. However, this is rarely the case in practice. For example,
Goode et al. (2014) find that higher socio-economic status has a positive
impact on the HAZ through greater health consciousness and better
household sanitation system. Therefore, we consider a normal mixture
distribution where

for positive weights summing to 1 in order to accommodate for a more

complex composition in the population. Each mixture component in (2.3)
corresponds to a particular type of growth pattern and each child belongs to
one of these subgroups. By clustering the children into different subgroups,
further analysis can then be done to identify risk factors which cause the
manifestation of certain growth behaviour.
Equation (2.3) requires the specification of the number of subgroups ,
which is often not known a priori in practice. Therefore, we employ a Bayesian
non-parametric approach to circumvent the model selection procedure in
modelling the distribution of the growth velocity . Conceptually, the number

of parameters in a Bayesian non-parametric model is set to infinity and a prior
distribution is posited on the infinite dimensional parameter space Θ. The
complexity of the model (referring to the value of in our setting) is then
adapted to the amount of information available in the dataset. One such prior
which has been widely used in various applications (da Silva, 2007; Blunsom et
al., 2008) is the Dirichlet process (DP) prior established in Ferguson (1973).
In order to illustrate the usefulness of the DP prior, we formulate our
problem of modelling the distribution of by a mixture distribution in terms

of a DP mixture model (Antoniak, 1974) in which

for = 1, . . . , where = ( , ) is the parameter of a normal distribution

specifying the mixture component associated with child and (, )
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