This session is concerned with summary statistics for interpoint correlation (i.e. dependence between points) and simulation envelopes.
The lecturer’s R script is available here (right click and save).

Exercise 1

The swedishpines dataset was recorded in a study plot in a large forest. We shall assume the pattern is stationary.

  1. Calculate the estimate of the \(K\)-function using Kest.

  2. Plot \(\widehat K(r)\) against \(r\)

  3. Plot \(\widehat K(r) - \pi r^2\) against \(r\).

  4. Calculate the estimate of the \(L\)-function and plot it against \(r\).

  5. Plot \(\widehat L(r) - r\) against \(r\).

  6. Calculate and plot an estimate of the pair correlation function using pcf.

  7. Draw tentative conclusions from these plots about interpoint interaction in the data.

Exercise 2

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?