Bayesian Score: Asymptotic Behavior

• The Bayesian score seems quite different from the MDL score

• However, the two scores are asymptotically equivalent

Theorem: If the prior P(? |G) is “well-behaved”, then

Proof:

• (Simple) Use Stirling’s approximation to ?( )

  • Applies to Bayesian networks with Dirichlet priors

• (General) Use properties of exponential models and Laplace’s method for approximating integrals

  • Applies to Bayesian networks with other parametric families

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