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In this research, we estimate that around $27.99(\pm2.15)\%$ of thepopulation has experienced wheezing before turning 1 in the United Kingdom.Furthermore, the Bernoulli Mixture Model classification is found to work bestwith $K=4$ clusters in order to better balance the separability of the clusterswith their explanatory nature, based on a cohort of $N=1184$. The probabilityof the group of parents in the $j$th cluster to say that their children havewheezed 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 eachcluster is $Z_n\ |\ R \sim \text{Categorical}(R)$, and the $n$th patientwheezed 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-Moptimization algorithm. We found that this clustering method groups efficientlythe patients with late-childhood wheezing, persistent wheezing, early-childhoodwheezing, and none or sporadic wheezing. Furthermore, we found that this methodis not dependent on the data-set, and can include data-sets with missingentries.

A Bernoulli Mixture Model to Understand and Predict Children Longitudinal Wheezing Patterns