stelfi
fits Hawkes and LogGaussian Cox Point Process models using Template Model Builder. See the package’s website for more details.
Introduced in Hawkes (1971) a Hawkes process is a selfexciting temporal point process where the occurrence of an event immediately increases the chance of another. We extend this to consider selfinhibiting process and a nonhomogeneous background rate. A logGaussian Cox process is a Poisson point process where the logintensity is given by a Gaussian random field. We extend this to a joint likelihood formulation fitting a marked logGaussian Cox model.
In addition, the package offers functionality to fit selfexciting 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).
From CRAN install.packages("stelfi")
or development version from GitHub:
require(devtools)
::install_github("cmjt/stelfi") devtools
The functions fit_hawkes()
and fit_hawkes_cbf()
fit selfexciting Hawkes (Hawkes AG., 1971) processes to temporal point pattern data.
The function fit_lgcp()
fit a logGaussian 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 selfexciting spatiotemporal Hawkes models to point pattern data. The selfexcitement is Gaussian in space and exponentially decaying over time. In addition, a GMRF can be included to account for latent spatial dependency.
Function  Key arguments 

fit_hawkes() 

fit_mhawkes() 

fit_hawkes_cbf() 
As
( \(^*\)Note, \(\texttt{mu}\) in 
fit_lgcp() 

fit_mlgcp() 

fit_stelfi() 

Function  Key arguments  Purpose 

get_coefs() 

Extract estimated parameter values from a fitted model. 
get_fields() 
As

Extract estimated mean, or standard deviation, of GMRF(s). 
get_weights() 

Calculate mesh weights. 
mesh_2_sf() 

Transforms mesh into a sf object. 
show_field() 

Plots spatial random field values. 
show_hawkes() 

Plot fitted Hawkes model. 
show_hawkes_GOF() 

Plot goodnessoffit metrics for a Hawkes model. 
show_lambda() 
As

Plot estimated spatial intensity from a fitted logGaussian Cox process model. 
sim_hawkes() 
As fit_hawkes() 
Simulate a Hawkes process. 
sim_lgcp() 
As fit_lgcp() 
Simulate a realisation of a logGaussian Cox process. 
Hawkes, AG. (1971) Spectra of some selfexciting 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.