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Keywords:

  • Cox point process;
  • filtering;
  • spatio-temporal modelling;
  • spike

Abstract

The paper deals with point processes in space and time and the problem of filtering. Real data monitoring the spiking activity of a place cell of hippocampus of a rat moving in an environment are evaluated. Two approaches to the modelling and methodology are discussed. The first one (known from literature) is based on recursive equations which enable to describe an adaptive system. Sequential Monte Carlo methods including particle filter algorithm are available for the solution. The second approach makes use of a continuous time shot-noise Cox point process model. The inference of the driving intensity leads to a nonlinear filtering problem. Parametric models support the solution by means of the Bayesian Markov chain Monte Carlo methods, moreover the Cox model enables to detect adaptivness. Model selection is discussed, numerical results are presented and interpreted. Copyright © 2009 John Wiley & Sons, Ltd.