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Spatio-temporal modelling of a cox point process sampled by a curve, filtering and inference. (English) Zbl 1192.60073
Spatio-temporal process point processes are important for various applications (seismoligy, forest fire ignition, epodemiology, neural systems and others). The paper deals with Cox point processes in time and space with Lévy based driven intensity. In particular, a Cox process sampled by a curve is discussed in detail due to its potential application in biology. The filtering of the driving intensity based on observed point process events is developed in space and time for a parametric model with a background driving compound Poisson field delimited by special test sets. Markov chain Monte Carlo “Metropolis within Gibbs” algorithm enables simultaneous filtering and parameter estimation. Posterior predictive distributions are used for model selection. The new approach to filtering is related to the residual analysis of spatio-temporal point processes.

60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62M30 Inference from spatial processes
60D05 Geometric probability and stochastic geometry
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