## Step-by-Step Solution Let's analyze each option in relation to **Gibbs sampling**: ### Option a > **Sampling all parameters simultaneously from their joint distribution** - **Explanation:** In Gibbs sampling, sampling from the *joint* distribution directly is usually not feasible, which is why Gibbs sampling is used in the first place. - **Conclusion:** **Incorrect** --- ### Option b > **Sampling each parameter sequentially from its full conditional distribution** - **Explanation:** This is the essence of Gibbs sampling. In each iteration, you sample each parameter, one at a time, from its full conditional distribution—i.e., the distribution of that parameter given the current values of the other parameters. - **Conclusion:** **Correct** --- ### Option c > **Using a random walk proposal for all parameters** - **Explanation:** This describes the Metropolis-Hastings algorithm, not Gibbs sampling. - **Conclusion:** **Incorrect** --- ### Option d > **Maximizing the posterior distribution** - **Explanation:** This describes Maximum a Posteriori (MAP) estimation, not a sampling method. - **Conclusion:** **Incorrect** --- ## **Final Answer** > **The correct answer is:** > > **b) Sampling each parameter sequentially from its full conditional distribution** --- ### **Summary Table** | Option | Is it correct? | Reason | |--------|:--------------:|---------------------------------------------------------------| | a | ❌ | Gibbs doesn't sample from the joint directly | | b | ✅ | This is exactly what Gibbs sampling does | | c | ❌ | Describes Metropolis-Hastings, not Gibbs | | d | ❌ | Describes MAP estimation, not a sampling method |