1. You are given a set of m objects that is divided into K groups, where the i t

Question

1. You are given a set of m objects that is divided into K groups, where the ith group is of size mi. If the goal is to obtain a sample of size n<m, what is the difference between the following two sampling schemes? (Assume sampling with replacement.)

(a) We randomly select n * mi / m elements from each group.

(b) We randomly select n elements from the data set, without regard for the group to which an object belongs.

2. Consider the problem of learning a classifier for forest fire mapping as described in question 3. The classification algorithm needs to be trained to recognize the signatures of burned pixels (and how they are different from non-burned ones). Typically, there is a huge imbalance in the number of fire (<0.1% of the total area) and non-fire pixels in any given region. Keeping this in mind, answer the following questions:

(a) What would happen if one were to randomly sample some locations (pixels) for training the classifier ignoring the presence/absence of fire at the location during sampling?

(b) How would stratified sampling help here?

Explanation / Answer

Answer: The scheme referred to in (a) is stratified sampling, which is
proportionate

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