  In this research, we estimate that around $27.99(\pm2.15)\%$ of the
population has experienced wheezing before turning 1 in the United Kingdom.
Furthermore, the Bernoulli Mixture Model classification is found to work best
with $K=4$ clusters in order to better balance the separability of the clusters
with their explanatory nature, based on a cohort of $N=1184$. The probability
of the group of parents in the $j$th cluster to say that their children have
wheezed during the $i$th age is assumed $P_{ij} \sim \text{Beta}(1/2, 1/2)$,
the probabilities of assignment to each cluster is $R \sim
\text{Dirichlet}_K(\alpha)$, the assignment of the $n$th patient to each
cluster is $Z_n\ |\ R \sim \text{Categorical}(R)$, and the $n$th patient
wheezed during the $i$th age is $X_{in}\ |\ P_{ij}, Z_n \sim
\text{Bernoulli}(P_{i,Z_n})$; where $i\in\{1,\dots,6\}$, $j\in\{1,\dots,K\}$,
and $n\in\{1,\dots, N\}$. The classification is then performed through the E-M
optimization algorithm. We found that this clustering method groups efficiently
the patients with late-childhood wheezing, persistent wheezing, early-childhood
wheezing, and none or sporadic wheezing. Furthermore, we found that this method
is not dependent on the data-set, and can include data-sets with missing
entries.
