文章基本信息

标题：Posterior Belief Assessment: Extracting Meaningful Subjective Judgements from Bayesian Analyses with Complex Statistical Models
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作者：Daniel Williamson ; Michael Goldstein
期刊名称：Bayesian Analysis
印刷版ISSN：1931-6690
电子版ISSN：1936-0975
出版年度：2015
卷号：10
期号：4
页码：877-908
DOI：10.1214/15-BA966SI
语种：English
出版社：International Society for Bayesian Analysis
摘要：In this paper, we are concerned with attributing meaning to the results of a Bayesian analysis for a problem which is sufficiently complex that we are unable to assert a precise correspondence between the expert probabilistic judgements of the analyst and the particular forms chosen for the prior specification and the likelihood for the analysis. In order to do this, we propose performing a finite collection of additional Bayesian analyses under alternative collections of prior and likelihood modelling judgements that we may also view as representative of our prior knowledge and the problem structure, and use these to compute posterior belief assessments for key quantities of interest. We show that these assessments are closer to our true underlying beliefs than the original Bayesian analysis and use the temporal sure preference principle to establish a probabilistic relationship between our true posterior judgements, our posterior belief assessment and our original Bayesian analysis to make this precise. We exploit second order exchangeability in order to generalise our approach to situations where there are infinitely many alternative Bayesian analyses we might consider as informative for our true judgements so that the method remains tractable even in these cases. We argue that posterior belief assessment is a tractable and powerful alternative to robust Bayesian analysis. We describe a methodology for computing posterior belief assessments in even the most complex of statistical models and illustrate with an example of calibrating an expensive ocean model in order to quantify uncertainty about global mean temperature in the real ocean.