CAS Exam MAS-II Spring 2019, Question 35
Study guide: Exam MAS-II
Suppose we want to model the standard deviation \sigma_i of a Gaussian distribution for each observation such that it is a function of a predictor variable x_i:
\begin{align*}
y_i &\sim \text{Normal}(\mu, \sigma_i^2) \\
\mu &\sim \text{Normal}(0, 25) \\
g(\sigma_i) &= \alpha + \beta x_i \\
\alpha &\sim \text{Uniform}(-5, 5) \\
\beta &\sim \text{Normal}(0, 2)
\end{align*}where g is a link function.
Three candidates for g are considered:
I. g(z) = \log(z)
II. g(z) = (z-1)^{\frac{1}{\tau}}, where \tau = 2
III. g(z) = e^{z}
Determine which of the candidate link functions would be appropriate for this model.
- A) None
- B) I and II only
- C) I and III only
- D) II and III only
- E) The answer is not given by (A), (B), (C), or (D)
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