CAS Exam MAS-II Fall 2019, Question 18
Study guide: Exam MAS-II
You wish to model the effect of gender on a random count outcome variable X. To achieve this, the variable for gender, denoted by F, is transformed such that it takes the value of 1 for females, otherwise it takes the value of 0. You fit the following model to your data:
\begin{align*}
X_i &\sim \text{Poisson}(\lambda_i) \\
\log(\lambda_i) &= \alpha + \beta_F F_i \\
\alpha &\sim \text{Normal}(0, 10) \\
\beta_F &\sim \text{Normal}(0, 10)
\end{align*}You are given the following output from the model:
| Mean | Standard Deviation | Median | |
|---|---|---|---|
\alpha |
2 | 0.5 | 1.9 |
\beta_F |
0.5 | 0.1 | 0.5 |
You obtain the following samples from the posterior distribution:
| Sample | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
\alpha |
1.9 | 1.8 | 2.1 | 2.1 | 2.2 | 2.1 | 1.7 |
\beta_F |
0.4 | 0.5 | 0.5 | 0.4 | 0.7 | 0.5 | 0.6 |
Calculate the estimate for the posterior median of the average female count based on this information.
- A) Less than 2.5
- B) Greater than or equal to 2.5 but less than 7.5
- C) Greater than or equal to 7.5 but less than 12
- D) Greater than or equal to 12 but less than 13
- E) Greater than or equal to 13
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