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On Bayesian and Decision-Theoretic Approaches to Statistical Prediction

  • Tapan K. Nayak
  • Abeer El-Baz
Chapter
  • 2.3k Downloads
Part of the Statistics for Industry and Technology book series (SIT)

Abstract

Let Y and Z be two random vectors with joint density f(y, z|θ), where θ∈Θ is an unknown parameter vector, and consider predicting Z based on y, the observed value of Y. We investigate Bayesian and decision-theoretic approaches to this problem, taking into account the loss function and the prior distribution of θ. Exploring connections between statistical prediction and decision theory, we find that a prediction problem can be reduced to a standard decision theory problem if the induced loss function is allowed to depend on the observed data y in addition to the unknown parameter θ and the decision d. In general, the predictive posterior density f(z|y) may not contain all information necessary for obtaining optimum predictions, but the posterior density f(θ|y) is adequate for that purpose. Some admissibility results are also discussed.

Keywords and phrases

Admissibility Bayes risk loss function predictive posterior distribution 

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Copyright information

© Birkhäuser Boston 2006

Authors and Affiliations

  • Tapan K. Nayak
    • 1
  • Abeer El-Baz
    • 1
  1. 1.George Washington UniversityWashington, DCUSA

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