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Bayesian point estimation and prediction

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Abstract

In the Bayesian viewpoint, point estimation and prediction are treated from a decision-making standpoint. If a loss function can be determined which associates a loss with every possible error of estimation or prediction, then the optimal estimator or predictor is that value which minimizes expected loss. In most applications, the loss function is assumed to be linear or quadratic in the error of estimation or prediction, although there are many practical situations in which these simple functions are quite inappropriate. In this paper, we investigate the properties of Bayesian point estimates under other loss functions; both the general case and two special cases (power and exponential loss functions) are considered. For the special cases, we also investigate the sensitivity of Bayesian point estimation and prediction to misspecification in the loss function and discuss the practical implications of the results.

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Authors and Affiliations

  1. University of Western Ontario, Canada

    Robert R. Britney & Robert L. Winkler

  2. Indiana University, USA

    Robert R. Britney & Robert L. Winkler

Authors
  1. Robert R. Britney
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  2. Robert L. Winkler
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Additional information

An earlier version of this paper was presented at the Annual Meeting of the American Statistical Association in New York, August 1968.

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Britney, R.R., Winkler, R.L. Bayesian point estimation and prediction. Ann Inst Stat Math 26, 15–34 (1974). https://doi.org/10.1007/BF02479801

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  • DOI: https://doi.org/10.1007/BF02479801

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