Question

Which of the following are true

Select one or more:

a. If you throw away a large number the initial samples (the burn in) from a Gibbs sampler what remains will approximate independent random samples from the stationary distribution.

b. Gibbs sampling can not be used to sample from a Bayesian network if we wish to condition on one of the variables taking a particular value.

c. Gibbs sampling is used when we wish to sample from a joint distribution when we only know the conditional distribution.

d. One of the advantages of using Gibbs sampling is that the samples it generates are independent of each other.

Answer 1

1. The statement is not true, because, the main idea of Gibbs sampling is to break the problem of sampling from the high-dimensional joint distribution into a series of samples from low-dimensional conditional distributions. Because these are done in a loop, samples are not independent and these dependence of the samples follow a Markov distribution.
2. This statement is true because the Bayesian approach to inference involves simply summarizing the posterior density using basic sample statistics.
3. This statement is true, because Gibbs sampling is applicable when the joint distribution is not known explicitly or is difficult to sample from directly, but the conditional distribution of each variable is known and is easy (or at least, easier) to sample from.
4. This statement is not true, as the samples are auto correlated.