This session is concerned with evelopes of summary statistics and Monte Carlo tests. The lecturerâ€™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.