Project 3, Part A: The Independent Random Process

The independent random process, or complete spatial randomness, operates according to the following two criteria when applied to point patterns:

1. events occur with equal probability anywhere; and
2. the place of occurrence of an event is not affected by the occurrence of other events.

The spatstat package provides a number of functions that will generate patterns according to IRP/CSR. The 'standard' one is rpoispp, which is actually a Poisson point process. This does not guarantee the same number of events in every realization as it uses a background process intensity to probabilistically create events. An alternative is the spatial point process function runifpoint, which guarantees to generate the specified number of events.

Begin by making sure that the spatstat library is loaded into RStudio:

> library(spatstat)

Then use the Poisson process to generate a point pattern. The rpoispp method takes one parameter, N, the number of events. N has been set to 100 in this case. Draw and examine the pattern in the Plots window.

> pp <- rpoispp(100)
> plot(pp)

After examining the pattern, use the up arrow key in the console, pressing it twice, to repeat the code that generates the pattern and then use the up arrow to repeat the line of code that draws the pattern. You should see the pattern change in the plots window. How similar or different is the second pattern?

It is often helpful to examine multiple realizations of a process to see whether the patterns exhibit any regularities. We can use R to generate and plot several realizations of the Poisson process at once so we can more easily compare them. The first line of code below sets a framework of three plots in one row for laying out multiple plots in the Plots window in RStudio. The subsequent lines generate the patterns and plot them.

> par(mfrow=c(1, 3))
> pp1 <- rpoispp(100)
> plot(pp1)
> pp2 <- rpoispp(100)
> plot(pp2)
> pp3 <- rpoispp(100)
> plot(pp3)