This session covers exploratory tools for investigating intensity.
The lecturer’s R script is available here (right click and save).

If you have not already done so, you’ll need to start R and load the spatstat package by typing

library(spatstat)

### Exercise 1

We will study a dataset that records the locations of Ponderosa Pine trees (Pinus ponderosa) in a study region in the Klamath National Forest in northern California. The data are included with spatstat as the dataset ponderosa.

1. assign the data to a shorter name, like X or P;

2. plot the data;

3. find out how many trees are recorded;

4. find the dimensions of the study region;

5. obtain an estimate of the average intensity of trees (number of trees per unit area).

### Exercise 2

The Ponderosa data, continued:

1. When you type plot(ponderosa), the command that is actually executed is plot.ppp, the plot method for point patterns. Read the help file for the function plot.ppp, and find out which argument to the function can be used to control the main title for the plot;

2. plot the Ponderosa data with the title Ponderosa Pine Trees above it;

3. from your reading of the help file, predict what will happen if we type

plot(ponderosa, chars="X", cols="green")

then check that your guess was correct;

4. try different values of the argument chars, for example, one of the integers 0 to 25, or a letter of the alphabet. (Note the difference between chars=3 and chars="+", and the difference between chars=4 and chars="X").

### Exercise 3

The dataset japanesepines contains the locations of Japanese Black Pine trees in a study region.

1. Plot the japanesepines data.

2. Use the command quadratcount to divide the study region of the Japanese Pines data into a 3x3 array of equal quadrats, and count the number of trees in each quadrat.

3. Most plotting commands will accept the argument add=TRUE and interpret it to mean that the plot should be drawn over the existing display, without clearing the screen beforehand. Use this to plot the Japanese Pines data, and superimposed on this, the 3x3 array of quadrats, with the quadrat counts also displayed.

4. Use the command quadrat.test to perform the $$\chi$$-square test of CSR on the Japanese Pines data.

5. Plot the Japanese Pines data, and superimposed on this, the 3x3 array of quadrats and the observed, expected and residual counts. Use the argument cex to make the numerals larger and col to display them in another colour.

### Exercise 4

Japanese Pines, continued:

1. Using density.ppp, compute a kernel estimate of the spatially-varying intensity function for the Japanese pines data, using a Gaussian kernel with standard deviation $$\sigma=0.1$$ units, and store the estimated intensity in an object D say.

2. Plot a colour image of the kernel estimate D.

3. Plot a colour image of the kernel estimate D with the original Japanese Pines data superimposed.

4. Plot the kernel estimate without the ‘colour ribbon’.

5. Try the following command

persp(D, theta=70, phi=25, shade=0.4)

and find the documentation for the arguments theta, phi and shade.