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What Bayes Has to Say About the Evidence Procedure

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  • David H. Wolpert
  • Charles E.M. Strauss

Abstract

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.

Suggested Citation

  • David H. Wolpert & Charles E.M. Strauss, 1995. "What Bayes Has to Say About the Evidence Procedure," Working Papers 95-02-026, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:95-02-026
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    1. David H. Wolpert, 1993. "On the Use of Evidence in Neural Networks," Working Papers 93-02-007, Santa Fe Institute.
    2. David H. Wolpert, 1994. "Bayesian Backpropagation Over I-O Functions Rather Than Weights," Working Papers 94-04-019, Santa Fe Institute.
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