ICAR-IASRI MSc and PhD Spatial Statistics, Geostatistics & Remote Sensing for Agriculture: practice questions

1 · Spatial data types: geostatistical, areal and point-pattern · easy

Soil pH is measured at 150 fixed grid points in a farm in order to map it everywhere. Which type of spatial data is this?

1. Geostatistical data
2. Point-pattern data, because each sample has coordinates
3. Time-series data, because samples were taken in sequence
4. Areal (lattice) data, because the farm is an area

2 · Spatial autocorrelation: Moran's I and Geary's C · hard

For the same layout of four plots in a row with yields 2, 4, 6 and 8 and binary neighbour weights between adjacent plots, what is Geary's C?

1. 0.60
2. 0.30
3. 1.00
4. 0.40

3 · Spatial autocorrelation: Moran's I and Geary's C · medium

Why are spatial weights matrices often row-standardised?

1. So Moran's I always equals zero
2. So the matrix becomes symmetric for every layout
3. So units without neighbours are dropped
4. So each unit's neighbours are averaged

4 · Variograms and their models · medium

For a second-order stationary process the sill is 10 and the semivariance at 30 m is 6. What is the correlation between values 30 m apart?

1. 4.0
2. 6.0
3. 0.4
4. 0.6

5 · Kriging: ordinary, universal and co-kriging · medium

When does co-kriging improve markedly on ordinary kriging of the target variable?

1. When the secondary variable is uncorrelated with the target
2. When both variables are measured at exactly the same points
3. When a correlated secondary variable is much denser
4. When the target variable has no spatial dependence

6 · Image classification as a statistical problem · medium

The maximum likelihood classifier for satellite images assumes that each land-cover class:

1. Occupies exactly the same number of pixels
2. Is independent of all other bands
3. Has equal mean reflectance in every band
4. Is multivariate normal in the bands

7 · Image classification as a statistical problem · hard

How do prior probabilities change maximum likelihood classification of pixels?

1. Priors make all classes equally likely
2. Pixels go to the class of highest posterior
3. Priors are used only for unsupervised clustering
4. Priors replace the class mean vectors entirely

8 · Accuracy assessment: error matrices and kappa; area estimation from maps · medium

With rows = map and columns = reference, the user's accuracy for wheat is 80/100 = 0.80. What does it mean to a map user?

1. 80 per cent of all pixels are correctly classified
2. 80 per cent of mapped wheat is truly wheat
3. 80 per cent of the real wheat area is mapped as wheat
4. The kappa coefficient for wheat is 0.80

9 · Accuracy assessment: error matrices and kappa; area estimation from maps · medium

A rare crop occupies 2 per cent of a mapped region. Which design for reference samples ensures enough samples to estimate its accuracy?

1. Simple random sampling of the whole region
2. Stratified random sampling by map class
3. Sampling only along roads for easy access
4. Using the classifier's training pixels again

10 · Satellite-based crop area and yield estimation · medium

Insurance payouts in a block depend on a satellite-assisted yield estimate. What is the most important statistical safeguard?

1. Releasing only the point estimate to avoid confusion
2. Adjusting estimates to match farmers' claims
3. Using the newest satellite without validation
4. A documented probability design with stated uncertainty