R code accompanying the paper Asymptotic approximation of the likelihood of stationary determinantal point processes with Frederic Lavancier.
The file "MLE_DPP.R" contains the function "MLEDPP" computing the asymptotic approximation of the MLE of common parametric families of stationnary DPPs and the function "Fisher_Info" computing the associated Fisher information matrix. The file "Estimator Comparison.R" gives examples of utilisation of the function "MLEDPP" as well as a way to reproduce the results of out paper. The file "Fisher IC.R" does the same for the function "Fisher_info".
The full syntax of the MLEDPP function is the following
MLEDPP = function(ppp, DPPfamily, startpar=NULL, sigma=NULL, edgecorr=FALSE, Trunc=50)
The main arguments are:
- ppp -> The observed point pattern, an object of class "ppp".
- DPPfamily -> The DPP family that is fitted to the data, it has to be either "Gauss", "Bessel", "Cauchy" or "Whittle-Matern".
The additional arguments are:
- startpar -> Optional. Initial value of alpha used in the optimization procedure. By default it is alpha_max/2 where alpha_max is the highest value of alpha for which the DPP is well-defined.
- sigma -> Must be specified for "Whittle-Matern" families only. The shape parametric of the family (called nu in dppMatern)
- edgecorr -> Logical. If 'TRUE' and the observation window is rectangular, it computes the periodic edge correction. If 'TRUE' and the observation window isn't rectangular, it computes the experimental edge correction described in Section 5.3 of our paper.
- Trunc -> Optional. Maximum truncation used for the computation of L_0 for all DPP families except Bessel.
The function returns an object of class "detpointprocfamily" corresponding to the DPP family fitted on the observed point pattern by the asymptotic approximation of the maximum likelihood estimator.
Currently, the approximated MLE is coded for stationnary DPPs on any window of R^2 with either a Gaussian-type kernel, a Bessel-type kernel with sigma=0, a Cauchy-type kernel with nu=1/2 or a Whittle-Matern-type kernel with a fixed shape parameter.
The full syntax of the Fisher_Info function is the following
Fisher_Info = function(ppp, DPPfamily, alpha_est, edgecorr=FALSE, Max_Trunc=50)
The main arguments are:
- ppp -> The observed point pattern, an object of class "ppp".
- DPPfamily -> The DPP family that is fitted to the data, it has to be either "Gauss", "Bessel" or "Cauchy".
- alpha_est -> The estimator of alpha obtained by maximum likelihood estimation.
The additional arguments are:
- edgecorr -> Logical. If 'TRUE' and the observation window is rectangular, it computes the periodic edge correction. If 'TRUE' and the observation window isn't rectangular, it computes the experimental edge correction described in Section 5.3 of our paper.
- Max_Trunc -> Optional. Maximum truncation used for the computation of L_0 for all DPP families except Bessel.
The function returns a 2x2 matrix corresponding to the Fisher Information matrix for the parameters (rho, alpha) of classical stationnary DPP families.
Currently, the approximated MLE is coded for stationnary DPPs on a rectangular window of R^2 with either a Gaussian-type kernel, a Bessel-type kernel with sigma=0 or a Cauchy-type kernel with nu=1/2.
This project depends on the following packages:
- spatstat
- stats
The following dependencies are optional, and only needed for parallelizing the task of testing the performance of the various estimators on DPPs that we consider.
- foreach
- doSNOW
- parallel