UE Temporal and spatial point process

Degrees incorporating this pedagocial element :


Point processes are a class of stochastic processes modelling random events in interaction. By event we can think of the time a neuron activates, the time a tweet has been retweeded, etc or the location of a tree in a forest, the impact of a lightning strike, etc. This course intends to provide an introduction to stochastic models which could cover such applications, to discuss the main characteristics of such processes, standard models (properties, simulation) and statistical procedures to infer them.

Part I (6 hours) - Temporal point processes

Definition and simulation of one-dimensional point processes (conditional/stochastic intensity); Likelihood and goodness-of-fit tests (illustration on the Poisson point process); Hawkes processes (estimation, goodness-of-fit, stationarity, ergodicity).

Part II (12 hours) - Spatial point processes

Definition and characterizationo of a spatial point process, intensity functions and conditional intensity functions; Poisson point process; Intensity estimation and summary statistics; Models for spatial point processes (Cox, determinantal and Gibbs point processes): characterization, simulation, statistical inference and validation. Keywords: stochastic processes; modelling of dependence; simulation and statistical inference; Poisson point process.