library(spatstat)In this exercise we work with the spatstat dataset
cells. First we show that a Poisson model is clearly
inadequate and then we investigate whether a determinantal point process
(DPP) model is a good fit.
Plot the cells dataset and briefly (1-2 lines) argue
why you donโt think a Poisson model is adequate for this data.
Generate 1999 realisations from a uniform point process model
with 42 points in the unit square (use runifpoint()) and
save them as sims.
Use the generated simulations (sims) as the
simulate argument in envelope.ppp() along with
your choice of summary statistic (argument fun) to make
envelopes for the cells data (also specify
savefuns = TRUE). Save the envelope as
env.
Load the GET package and make the global rank
envelope test using the envelope env you generated above
and plot the result.
Fit a Bessel DPP to the cells data using
dppm() (hint: dppBessel() is
useful).
Generate 39 realisations from the fitted Bessel DPP model model
in the unit square (use simulate()) and save them as
sims2.
Use the generated simulations (sims2) as the
simulate argument in envelope.ppp() with
argument fun = pcf to make envelopes for the
cells data. Save the envelope as
env2.
Plot the envelopes and add the theoretical pcf for this DPP model
to the plot (hint: extract pcf with pcfmodel() and
add to existing plot with plot(, add = TRUE)).
Does the mean pcf from the simulations agree with the theoretical pcf? Does the empirical pcf?
(Optional) Make global envelopes based on nsim = 39
simulations. Try both without specifying ginterval and with
ginterval = c(.02,.25). What is the difference?
(Optional) Try to (briefly) explain the large value of g(r) around r = 0.15.