sppmix: Poisson point process modeling using normal mixture models

Assessment of e-Social Activity in Psychiatric Patients

“…The next step is to find the estimates of the N (conditional) intensity functions. Looking carefully at (25), it is easy to note that the optimization with respect to each (conditional) intensity is independent from the others, and ignoring constant terms is equivalent to…”

“…In other words, it would be assumed that the patient always describes the same type of behavior; which may not be true, due to, e.g., potential relapses and disease remissions, or simply due to weekends and holidays. Although mixtures of Poisson point processes have been successfully applied in other fields, like vehicular accident data [20], insurance claims [21], economy [22], [23], RNA sequencing [24], or earthquake modeling [25], to the best of our knowledge, there is no previous work that has used them for the assessment of e-social activity of psychiatric patients. Actually, the use of these mixture models in psychiatry poses a series of challenges that have not been addressed in the aforementioned works.…”

Cox Point Processes: Why One Realisation Is Not Enough

“…For the development, application, evaluation and algorithms for problems involving mixture models, we refer to Green (1995), Richardson & Green (1997), Stephens (2000), Cappé et al (2003), Robert & Casella (2004), Jasra et al (2005), Dellaportas & Papageorgiou (2006), Micheas et al (2012), Micheas (2014), Zhou et al (2015), Micheas & Chen (2018) and the references therein. Finite mixtures are quite applicable in practice, because they can provide inference for individual features of an intensity surface (e.g.…”

“…For recent contributions in the literature, see Stephens (), Celeux et al (), Jasra et al (), Marin et al (), Yao (), Keribin et al () and the references therein. We address the label switching problem using the approach in Micheas & Chen () by finding the best permutation of the posterior realisations either via an identifiability constraint or by a decision theoretic approach. Alternatively, we obtain and propose the maximum a posteriori (MAP) estimates of the parameters, which are not affected by label switching.…”

“…The RMCP can be simulated first by using function sppmix::rmixsurf from the sppmix R package (Micheas & Chen, ) to generate a random mixture intensity and then using function sppmix::rsppmix to generate the point pattern. Model fitting is performed via a Bayesian framework using the function sppmix::est_mix_damcmc (using the DAMCMC approach) to estimate the mixture parameters with a fixed number of components, or function sppmix::est_mix_bdmcmc (using the BDMCMC approach) for a random number of components.…”