stelfi | R Documentation |
Fit Hawkes and log-Gaussian Cox process models with extensions. Introduced in Hawkes (1971) a Hawkes process is a self-exciting temporal point process where the occurrence of an event immediately increases the chance of another. We extend this to consider self-inhibiting process and a non-homogeneous background rate. A log-Gaussian Cox process is a Poisson point process where the log-intensity is given by a Gaussian random field. We extend this to a joint likelihood formulation fitting a marked log-Gaussian Cox model. In addition, the package offers functionality to fit self-exciting spatiotemporal point processes. Models are fitted via maximum likelihood using 'TMB' (Template Model Builder) (Kristensen, Nielsen, Berg, Skaug, and Bell, 2016). Where included 1) random fields are assumed to be Gaussian and are integrated over using the Laplace approximation and 2) a stochastic partial differential equation model, introduced by Lindgren, Rue, and Lindström. (2011), is defined for the field(s).
The functions fit_hawkes
and fit_hawkes_cbf
fit self-exciting Hawkes (Hawkes AG., 1971) processes to temporal point pattern data.
The function fit_lgcp
fit a log-Gaussian Cox process to
either spatial or spatiotemporal point pattern data. If a spatiotemporal
model is fitted a AR1 process is assumed for the temporal progression.
The function fit_mlgcp
fits a joint likelihood model between
the point locations and the mark(s).
The function fit_stelfi
fits self-exciting spatiotemporal
Hawkes models to point pattern data. The self-excitement is Gaussian in space
and exponentially decaying over time. In addition, a GMRF can be included
to account for latent spatial dependency.
Hawkes, AG. (1971) Spectra of some self-exciting and mutually exciting point processes. Biometrika, 58: 83–90.
Lindgren, F., Rue, H., and Lindström, J. (2011) An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 73: 423–498.
Kristensen, K., Nielsen, A., Berg, C. W., Skaug, H., and Bell B. M. (2016). TMB: Automatic Differentiation and Laplace Approximation. Journal of Statistical Software, 70: 1–21.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.