University of Groningen, The Netherlands.
Br J Math Stat Psychol. 2013 Feb;66(1):68-75. doi: 10.1111/j.2044-8317.2012.02067.x. Epub 2012 Sep 28.
Gelman and Shalizi (2012) criticize what they call the 'usual story' in Bayesian statistics: that the distribution over hypotheses or models is the sole means of statistical inference, thus excluding model checking and revision, and that inference is inductivist rather than deductivist. They present an alternative hypothetico-deductive approach to remedy both shortcomings. We agree with Gelman and Shalizi's criticism of the usual story, but disagree on whether Bayesian confirmation theory should be abandoned. We advocate a humble Bayesian approach, in which Bayesian confirmation theory is the central inferential method. A humble Bayesian checks her models and critically assesses whether the Bayesian statistical inferences can reasonably be called upon to support real-world inferences.
Gelman 和 Shalizi(2012)批评了他们所谓的贝叶斯统计学中的“常见故事”:即假设或模型的分布是统计推断的唯一手段,从而排除了模型检验和修正,并且推断是归纳的而不是演绎的。他们提出了一种替代的假设演绎方法来弥补这两个缺点。我们同意 Gelman 和 Shalizi 对常见故事的批评,但不同意是否应该放弃贝叶斯确认理论。我们主张采取谦逊的贝叶斯方法,其中贝叶斯确认理论是中心推理方法。谦逊的贝叶斯人会检查她的模型,并批判性地评估是否可以合理地利用贝叶斯统计推断来支持对现实世界的推断。