Mixtures of heterogeneous Poisson processes for the assessment of e-social activity in mental health

Abstract

This work introduces a novel method to assess the social activity maintained by psychiatric patients using information and communication technologies. In particular, we jointly model using point processes the e-social activity patterns from two heterogeneous sources: the usage of phone calls and social and communication apps. We propose a nonhomogeneous Poisson mixture model with periodic (circadian) intensity function using a truncated Fourier series expansion, which is inferred using a trust-region algorithm, and it is able to cope with the different daily patterns of a person. The analysis of the usage of phone calls and social and communication apps of a cohort of 164 patients reveals that 25 patterns suffice to characterize their daily behavior.