This session is concerned with evelopes of summary statistics and Monte Carlo tests. The lecturer’s R script is available here (right click and save).
For the swedishpines data:
Plot the (K) function along with pointwise envelopes from 39 simulations of CSR:
plot(envelope(swedishpines, Kest, nsim=39))
Plot the (L) function along with pointwise envelopes from 39 simulations of CSR.
Plot the (L) function along with simultaneous envelopes from 19 simulations of CSR, using ginterval=c(0,0.5).
Plot the (L) function for along with simultaneous envelopes from 99 simulations of CSR using ginterval=c(0,0.5). What is the significance level of the associated test?
To understand the difficulties with the (K)-function when the point pattern is not spatially homogeneous, try the following experiment (like in the previous lab session).
Generate a simulated realisation of an inhomogeneous Poisson process, e.g.
X <- rpoispp(function(x,y){ 200 * exp(-3 * x) })
Compute simulation envelopes (of your favorite type) of the (K)- or (L)-function under CSR. They may well indicate significant departure from CSR.
Fit a Poisson point process model to the japanesepines data with log-quadratic trend (formula ~polynom(x,y,2)). Plot the (L)-function of the data along with simultaneous envelopes from 99 simulations of the fitted model.