Lab 7: Envelopes and Monte Carlo tests

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).

Exercise 1

For the swedishpines data:

  1. Plot the K function along with pointwise envelopes from 39 simulations of CSR:

    plot(envelope(swedishpines, Kest, nsim=39))

  2. Plot the L function along with pointwise envelopes from 39 simulations of CSR.

  3. Plot the L function along with simultaneous envelopes from 19 simulations of CSR, using ginterval=c(0,0.5).

  4. 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?

Exercise 2

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).

  1. Generate a simulated realisation of an inhomogeneous Poisson process, e.g.

    X <- rpoispp(function(x,y){ 200 * exp(-3 * x) })

  2. Compute simulation envelopes (of your favorite type) of the K- or L-function under CSR. They may well indicate significant departure from CSR.

  3. 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.