Mixture Modeling for Marked Poisson Processes

Mixture Modeling for Marked Poisson Processes

We propose a general modeling framework for marked Poisson processes observed over time or space. The modeling approach exploits the connection of the nonhomogeneous Poisson process intensity with a density function. Nonparametric Dirichlet process mixtures for this density, combined with nonparametric or semiparametric modeling for the mark distribution, yield flexible prior models for the mar...

Poisson processes (and mixture distributions)

Markov-modulated Marked Poisson Processes for Check-in Data

We develop continuous-time probabilistic models to study trajectory data consisting of times and locations of user ‘check-ins’. We model the data as realizations of a marked point process, with intensity and mark-distribution modulated by a latent Markov jump process (MJP). We also include user-heterogeneity in our model by assigning each user a vector of ‘preferred locations’. Our model extend...

Markov-modulated marked Poisson processes for check-in data [draft]

We develop continuous-time probabilistic models to study trajectory data consisting of times and locations of user ‘check-ins’. We model these as realizations of a marked point process, with intensity and mark-distribution modulated by a latent Markov jump process (MJP). We extend this Markov-modulated marked Poisson process to include user-heterogeneity by assigning users vectors of ‘preferred...

Local Block Bootstrap for Inhomogeneous Poisson Marked Point Processes

The asymptotic theory for the sample mean of a marked point process in d dimensions is established, allowing for the possibility that the underlying Poisson point process is inhomogeneous. A novel local block bootstrap method for resampling inhomogeneous Poisson marked point processes is introduced, and its consistency is proven for the sample mean and related statistics. Finite-sample simulati...