Customer churn prediction is a valuable task in many industries. In telecommunications it presents great challenges, given the high dimensionality of the data, and how difficult it is to identify underlying frustration signatures, which may represent an important driver regarding future churn behaviour. Here, we propose a novel Bayesian hierarchical joint model that is able to characterise customer profiles based on how many events take place within different television watching journeys, and how long it takes between events. The model drastically reduces the dimensionality of the data from thousands of observations per customer to 11 customer-level parameter estimates and random effects. We test our methodology using data from 40 BT customers (20 active and 20 who eventually cancelled their subscription) whose TV watching behaviours were recorded from October to December 2019, totalling approximately half a million observations. Employing different machine learning techniques using the parameter estimates and random effects from the Bayesian hierarchical model as features yielded up to 92% accuracy predicting churn, associated with 100% true positive rates and false positive rates as low as 14% on a validation set. Our proposed methodology represents an efficient way of reducing the dimensionality of the data, while at the same time maintaining high descriptive and predictive capabilities. We provide code to implement the Bayesian model at https://github.com/rafamoral/profiling_tv_watching_behaviour.

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Many studies have shown that the protection of the host Acyrthosiphon pisum (Hemiptera, Aphididae) against the parasitoid Aphidius ervi (Hymenoptera, Braconidae) is conferred by the interaction between the secondary endosymbiont Hamiltonella defensa and the bacteriophage APSE (Acyrthosiphon pisum secondary endosymbiont). This interaction consists of the production of toxins by the endosymbiont's molecular machinery, which is encoded by the inserted APSE genes. The toxins prevent the development of the parasitoid's egg, conferring protection for the host. However, the effects of this microscopic interaction on host-parasitoid dynamics are still an open question. We presented a new mathematical model based on the bacteriophage effect on parasitism resistance. We identified that the vertical transmission of the bacteriophage and the host survival after the parasitoid attack are potential drivers of coexistence. Also, we showed that the vertical transmission of H. defensa is proportional to the time that the protected population became extinct. Our results showed that the protected and unprotected hosts' survival after the parasitoid attack is fundamental to understanding the equilibrium of long host-parasitoid dynamics. Finally, we illustrated our model considering its parameters based on experiments performed with A. pisum biotypes Genista tinctoria and Medicago sativa.