Bayesian Calculations

  • Christian P. Robert
Part of the Springer Texts in Statistics book series (STS)

Abstract

Before concluding this book, we need to discuss a practical aspect of the Bayesian paradigm, namely, the computation of Bayes estimators. The ultimate simplicity of the Bayesian approach is that, given a loss function L and a prior distribution π, the Bayes estimate associated with an observation x is the (usually unique) decision d minimizing the posterior loss
$$ L\left( {\pi ,d\left| x \right.} \right) = \int_\theta {L\left( {\theta ,d} \right)\pi \left( {\theta \left| x \right.} \right)d\theta .} $$
(9.1)

Keywords

Posterior Distribution Prior Distribution Conditional Distribution Gibbs Sampling Exponential Family 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Christian P. Robert
    • 1
  1. 1.URA CNRS 1378 — Dépt. de Math.Université de RouenMont Saint Aignan CedexFrance

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