A small collection of tools for model evaluation in point pattern statistics.

For data analysis there is an extensive R-package spatstat.

Currently implemented

• K and pcf with "translate" edge correction
• F and G using Kaplan-Meier estimator
• Global envelope based on Extreme Rank Length
• SimpleSequentialInhibition
• PointPattern type with convert to and from spatstat::ppp

Summary function estimators return only a vector of estimated values that is convenient for computation but not for plotting.

using PointPatternStatistics
window = (x=(0,1), y=(0,1))
xy = [(rand(), rand()) for _ in 1:300]
r = 0:0.01:0.25
pp = PointPattern(xy, window)
pcf(pp, r)
Kest(pp, r)
Fest(pp, r)
Gest(pp, r)

xys = [[(rand(), rand()) for _ in 1:30] for _ in 1:2499]
A = [pcf(PointPattern(xy, window), r) for xy in xys]
globalenvelope(A)

using PointPatternStatistics
using RCall
@rimport spatstat

x = rand(SimpleSequentialInhibition(0, 30, 0, 20, 1))
R"plot"(x)
spatstat.fryplot(x)

Stoyan, D., & Stoyan, H. (1994). Fractals, random shapes, and point fields: methods of geometrical statistics (Vol. 302). John Wiley & Sons Inc.

Adrian Baddeley, Ege Rubak, Rolf Turner (2015). Spatial Point Patterns: Methodology and Applications with R. London: Chapman and Hall/CRC Press, 2015. URL http://www.crcpress.com/Spatial-Point-Patterns-Methodology-and-Applications-with-R/Baddeley-Rubak-Turner/9781482210200/

Baddeley, A.J. and Gill, R.D. Kaplan-Meier estimators of interpoint distance distributions for spatial point processes. Annals of Statistics 25 (1997) 263-292.

Myllymäki, M., Mrkvicka, T., Grabarnik, P., Seijo, H. and Hahn, U. (2017). Global envelope tests for spatial processes. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 79: 381-404. doi: 10.1111/rssb.12172