What Bayes has to say about the evidence procedure

  • Wolpert D
  • Strauss C
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The ``evidence'' procedure for setting
hyperparameters is essentially the same as the
techniques of ML-II and generalized maximum
likelihood. Unlike those older techniques however,
the evidence procedure has been justified (and
used) as an approximation to the hierarchical
Bayesian calculation. We use several examples to
explore the validity of this justification. Then we
derive upper and (often large) lower bounds on the
difference between the evidence procedure's answer
and the hierarchical Bayesian answer, for many
different quantities. We also touch on subjects
like the close relationship between the evidence
procedure and maximum likelihood, and the
self-consistency of deriving priors by
``first-principles'' arguments that don't set the
values of hyperparameters.

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  • DH Wolpert

  • CEM Strauss

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