Bayesian Score: Asymptotic Behavior

Consequences:

• Bayesian score is asymptotically equivalent to MDL score

  • The terms log P(G) and description length of G are constant and thus they are negligible when M is large.

• Bayesian score is consistent

  • Follows immediately from consistency of MDL score

• Observed data eventually overrides prior information

  • Assuming that the prior does not assign probability 0 to some parameter settings

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