mimetic: Univariate point pattern simulation by mimetic point process

Description

Simulates replicates of an observed univariate point pattern by stochastic optimization of its L-function properties.

Usage

mimetic(x,upto=NULL,by=NULL,prec=NULL,nsimax=3000,conv=50)

Arguments

either a ("fads", "kfun") object or a "spp" object of type "univariate" defining a spatial point pattern in a given sampling window (see kfun or spp<

upto

(optional) maximum radius of the sample circles when x is a "spp" object.

(optional) interval length between successive sample circles radii when x is a "spp" object.

prec

precision of point coordinates generated during simulations when x is a "spp" object. By default prec=0.01 or the value used in fonction kfun when x is a ("fads", "kfun") object.

nsimax

maximum number of simulations allowed. By default the process stops after nsimax=3000 if convergence is not reached.

conv

maximum number of simulations without optimization gain (convergence criterion).

Value

A list of class "mimetic" with essentially the following components:
callthe function call.
fadsan object of class ("fads", "mimetic") with 2 components:
..ra vector of regularly spaced out distances corresponding to seq(by,upto,by).
..la dataframe with 2 components:
.. ..obsa vector of values of the L-function estimated for the initial observed pattern
.. ..sima vector of values of the L-function estimated for the simulated pattern
sppa object of class "spp" corresponding to the simulated point pattern (see spp).
theoa vector of theoretical values, i.e. Simpson $D$ for all the points.
costa vector of the successive values of the cost function.

encoding

latin1

Details

Function mimetic uses a stepwise depletion-replacement algorithm to generate a point pattern whose L-function is optimized with regards to an observed one, following the mimetic point process principle (Goreaud et al. 2004). Four points are randomly deleted at each step of the process and replaced by new points that minimize the following cost function:||$Lobs(r) - Lsim (r)$||)^2. The simulation stops as soon as the cost fonction doesn't decrease after conv simulations or after a maximum of nsimax simulations. The process apply to rectangular, circular or comlex sampling windows (see spp). There exist a plot method that displays diagnostic plots, i.e. the observed and simulated L-function, the simulated point pattern and the successive values of the cost function.

References

Goreaud F., Loussier, B., Ngo Bieng, M.-A. & Allain R. 2004. Simulating realistic spatial structure for forest stands: a mimetic point process. In Proceedings of Interdisciplinary Spatial Statistics Workshop, 2-3 December, 2004. Paris, France.

Examples

Run this code

data(BPoirier)
  BP<-BPoirier
  # performing point pattern analysis in a rectangle sampling window
  swr <- spp(BP$trees, win=BP$rect)
  plot(swr)
  
  # performing the mimetic point process from "spp" object
  mimswr <- mimetic(swr, 25, 1)
  plot(mimswr)

   # performing the mimetic point process from "fads" object
  mimkswr <- mimetic(kfun(swr, 25, 1))
  plot(mimkswr)

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