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What is Markov chain Monte Carlo sampling in a network?

  • A.Sampling from a chain of networks of increasing complexity
  • B.Generating independent samples from the full joint distribution
  • C.Sampling only along the Markov chain formed by the evidence
  • D.Sampling each variable in turn given its Markov blanket

Answer: D

Gibbs sampling starts from an arbitrary assignment and repeatedly resamples one variable given its blanket, and the sequence converges to the posterior. The samples are dependent, which is the price of avoiding rejection. Complexity ladders and independent sampling are different schemes. That a local update rule produces globally correct samples in the limit is a remarkable result and it is what makes the method practical for large networks.

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