The list

(a) to

(d) below describes some real situations. Each situation can be modelled by one of the following approaches:

Option Q is technically known as a mixture model, because the observed outcomes are a mixture of observations from different classes.

Option R is called a regression model.

P. Binomial model.

Q. Indirect binomial model where the outcome of interest is not observed directly.

R. Best-fit line.

S. Poisson model.

Match each of the situations below to the most suitable model descriptions from P, Q, R, and S. Briefly explain your answers.

a. X1, X2, . . . , Xn are the number of car accidents on a motorway in years 1, 2, . . . , n. We want to estimate the overall accident rate.

b. X1, X2, . . . , Xn are observations on n retired builders. Each Xi is 0 or 1 specifying whether the builder has mesothelioma, which is a rare cancer associated with exposure to asbestos. We know rates of mesothelioma with and without asbestos exposure. We want to estimate the rate of asbestos exposure.

Asbestos is a toxic dust found in old buildings.

c. X1, X2, . . . , Xn are the number of customers of a business in years 1, 2, . . . , n. We want to investigate trends in the number of customers over time.

d. X1, X2, . . . , Xn are observations on n students in a course.
Each Xi is 0 or 1 according to whether the student passes the course. We want to estimate the pass rate.