CAS Exam MAS-II Spring 2019, Question 34
Study guide: Exam MAS-II
You want to check your software's implementation of the Hamiltonian Monte Carlo algorithm (HMC) to ensure is working properly for a model with a single parameter, \theta. The software's HMC implementation has the following properties:
- The derivative of the potential function with respect to
\thetais -2.2 - Step size,
\epsilon, is 0.02 - Number of steps,
L, is 50 - The standard deviation,
s, of the normal momentum distribution is 0.05
At the end of the L steps for a particular HMC iteration, you compute the table of densities below. The current column contains densities at the start of the iteration and the proposed column contains densities at the end of the iteration.
| current | proposed | |
|---|---|---|
| likelihood | 0.025 | 0.021 |
| prior | 0.150 | 0.100 |
| momentum | 0.070 | 0.068 |
Calculate the probability of rejecting the proposed \theta at the end of this iteration.
- A) Less than 0.25
- B) Greater than or equal to 0.25 but less than 0.50
- C) Greater than or equal to 0.50 but less than 0.75
- D) Greater than or equal to 0.75 but less than 1.00
- E) 1.00
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