Complete the following exercises within the lab period and submit to Canvas before leaving. In addition to the points detailed below, 5 points are assigned to the quality of the annotation and to the ‘cleanliness’ of the code and resulting pdf document.

Exercise 1 – 2 points

We will again be working with the BC Parks dataset, which contains information on the locations of Provincial Parks in British Columbia. The parks belong to 5 different regions. There is also information on elevation (in m) contained within the dataset.

  • Import the BC park locations dataset and convert the data to a ppp object (being sure to include information on regions as marks). – 0.5 point(s)
  • Plot the resulting ppp object. The marks need to be visually distinct. – 0.5 point(s)
  • Inspect the spatial distribution of parks. Do you expect the process to be homogeneous? Justify why you came to this expectation. – 1 point(s)

Note: You will need to load the maptools or sp packages and make use of the as.owin() function.

Exercise 2 – 2 points

  • Under an assumption of homogeneity, what is the intensity of parks/km\(^2\) in BC? – 1 point(s)
  • Is the estimated intensity trustworthy? Why/why not? – 1 point(s)

Hint: see ?rescale

Exercise 3 – 2 points

  • Use a quadrat test to determine whether the assumption of homogeneity is met. – 1 point(s) Note: Be sure to set the number of quadrats appropriately, to avoid issues with the quadrat test.
  • Visualise both the quadrats and estimated intensity, being sure to include the points in each figure. – 1 point(s)
  • Is the estimated intensity from exercise 2 trustworthy, and why? – 1 point(s)

Exercise 4 – 4 points

  • Estimate the intensity using kernel estimation with likelihood cross validation bandwidth selection. – 1 point(s)
  • Perform hotspot analysis to identify locations of elevated intensity. – 1 point(s)
  • Visualise the output (be sure to include the window). – 1 point(s)
  • Based on the estimated intensity and hotspot analysis, where would choose to go if you were planning a vacation to tour different provincial parks. – 1 point(s)

Exercise 5 – 3 points

  • Estimate \(\rho\) for the locations of parks as a function of elevation. – 1 point(s)
  • Plot \(\rho\) vs. elevation. Be sure that the x-axis for elevation does not go below 0. – 1 point(s)
  • Do you think that there is a relationship between elevation and park intensity? Use the results/data to support your statements. – 0.5 point(s)
  • Would you be more or less likely to find a park at 1500m compared to the average intensity of parks across B.C.? Why? – 0.5 point(s)

Note: Estimating rho can be slow (\(\sim\) 1-2 min). Be sure to leave enough time for the document to knit.

Exercise 6 – 5 points

  • Using Ripley’s \(K\)-function, test for a significant (i.e., \(\alpha\) = 0.05) correlation between park locations. – 4 point(s)
  • Is there any evidence of correlations in park locations? Why? – 1 point(s)

Notes: Use border corrections (i.e., correction="border") and be sure the estimators assumptions are being met.

Exercise 7 – 3 points

  • Using simulation envelopes, estimate both the homogeneous and inhomogeneous pair correlation functions. – 1.5 point(s)
  • Visualise the results. – 0.5 point(s)
  • Are the estimates comparable? Which of these would you use to draw conclusions about the clustering of provincial parks? – 0.5 point(s)
  • Are parks in BC clustered? – 0.5 point(s)

Note: These steps can be slow (\(\sim\) 1-2 min). Be sure to leave enough time for the document to knit.

Exercise 8 – 3 points

  • Based on these descriptive statistics, what have you learned about the spatial distribution of parks in BC?