CAS Exam MAS-II Spring 2019, Question 27
Study guide: Exam MAS-II
A multilevel model with varying intercepts for class is fit to a dataset that includes two other independent variables, X_1 and X_2. The model is specified below.
\begin{align*}
y_i &\sim \text{Poisson}(\lambda_i) \\
\ln(\lambda_i) &= \alpha + \alpha_{class[i]} + \beta_1 X_{1i} + \beta_2 \ln(X_{2i}) \\
\alpha &\sim \text{Normal}(0,\, 2) \\
\alpha_{class} &\sim \text{Normal}(0,\, \sigma^2_{class}) \\
\beta_1 &\sim \text{Normal}(0,\, 1) \\
\beta_2 &\sim \text{Normal}(0,\, 10) \\
\sigma_{class} &\sim \text{HalfCauchy}(0,\, 1)
\end{align*}An actuary wants to obtain a prediction for an unobserved, average class when x_1 = 0.28 and x_2 = 122.4.
Determine the minimum number of posterior distributions that the actuary needs to consider to obtain a prediction.
- A) 2 or fewer
- B) 3
- C) 4
- D) 5
- E) 6 or more
No current syllabus covers this question; it is kept for the record.
Answer this question and see the worked solution