On the choice of a noninformative prior for Bayesian inference of discretized normal observations

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• 作者：Clemens Elster (1) clemens.elster@ptb.de
  Ignacio Lira (2) ilira@ing.puc.cl
• 关键词：Bayesian inference – ; Noninformative prior – ; Grouped data
• 刊名：Computational Statistics
• 出版年：2012
• 出版时间：June 2012
• 年：2012
• 卷：27
• 期：2
• 页码：219-235
• 全文大小：363.6 KB
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• 作者单位：1. Physikalisch-Technische Bundesanstalt (PTB), Braunschweig, Berlin, Germany2. Pontificia Universidad Cat贸lica de Chile, Santiago, Chile
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Statistics
  Statistics
  Probability and Statistics in Computer Science
  Probability Theory and Stochastic Processes
  Economic Theory
  
• 出版者：Physica Verlag, An Imprint of Springer-Verlag GmbH
• ISSN：1613-9658

文摘

We consider the task of Bayesian inference of the mean of normal observations when the available data have been discretized and when no prior knowledge about the mean and the variance exists. An application is presented which illustrates that the discretization of the data should not be ignored when their variability is of the order of the discretization step. We show that the standard (noninformative) prior for location-scale family distributions is no longer appropriate. We work out the reference prior of Berger and Bernardo, which leads to different and more reasonable results. However, for this prior the posterior also shows some non-desirable properties. We argue that this is due to the inherent difficulty of the considered problem, which also affects other methods of inference. We therefore complement our analysis by an empirical Bayes approach. While such proceeding overcomes the disadvantages of the standard and reference priors and appears to provide a reasonable inference, it may raise conceptual concerns. We conclude that it is difficult to provide a widely accepted prior for the considered problem.