CAS Exam MAS-II Fall 2019, Question 21
Study guide: Exam MAS-II
A regression model for the number of automobile accidents, Y_i, for driver i assumes a zero-inflated Poisson (ZIPoisson) distribution with p_i being the probability of zero. The model is shown below.
\begin{align*}
Y_i &\sim \text{ZIPoisson}(\lambda_i,\ p_i) \\
\ln(\lambda_i) &= \beta_0 + \beta_1 x_{1i} \\
\text{logit}(p_i) &= \alpha_0 + \alpha_1 x_{1i} \\
\beta_0 &\sim \text{Normal}(0,\ 10) \\
\beta_1 &\sim \text{Normal}(0,\ 1) \\
\alpha_0 &\sim \text{Normal}(0,\ 2) \\
\alpha_1 &\sim \text{Normal}(0.5,\ 0.5)
\end{align*}After sufficient warmup, two samples (sample 1 and sample 2) from the posterior distribution are taken and provided in the table below:
\beta_0 |
\beta_1 |
\alpha_0 |
\alpha_1 |
|
|---|---|---|---|---|
| sample 1 | -0.96 | 0.13 | -2.75 | 0.90 |
| sample 2 | 0.55 | -0.23 | -0.63 | 0.32 |
Compute the mean probability of a driver having 0 automobile accidents when x_1 = 2.0 from the posterior predictive distribution.
- A) Less than 0.75
- B) Greater than or equal to 0.75 but less than 0.80
- C) Greater than or equal to 0.80 but less than 0.85
- D) Greater than or equal to 0.85 but less than 0.90
- E) Greater than or equal to 0.90
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