VIPSolutionsQuestion of Stats and Probability In Gibbs sampling, each iteration typically involves: 2) Sampling all parameters simultaneously from their joint distribution b) Sampling each parameter sequentially from its full conditional distribution ©) Using a random walk proposal for all parameters d) Maximizing the posterior distribution
Question:
Question of Stats and Probability
In Gibbs sampling, each iteration typically involves:
2) Sampling all parameters simultaneously from their joint distribution
b) Sampling each parameter sequentially from its full conditional distribution
©) Using a random walk proposal for all parameters
d) Maximizing the posterior distribution
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Asked by: naveen kumae
Created at: 2026-01-21 04:52:54
Asked by: naveen kumae
Created at: 2026-01-21 04:52:54
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## Answer
The correct answer is:
**b) Sampling each parameter sequentially from its full conditional distribution**
### Explanation
In Gibbs sampling, each parameter is sampled **one at a time**, conditioned on the current values of all the other parameters. This is done using the full conditional distribution for each parameter. So, the process is sequential and conditional, not simultaneous (a), not using a random walk proposal (c), and not maximizing the posterior (d).
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**Summary Table:**
| Option | Description | Correct? |
|--------|-----------------------------------------------------------|----------|
| a | Simultaneous joint sampling | No |
| b | Sequential sampling from full conditional | **Yes** |
| c | Random walk proposal | No |
| d | Maximizing posterior | No |
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