For many years it was routine to use equal model prior probabilities in Bayesian model uncertainty analysis. At least twenty years ago it became clear that this was problematic, leading to support of much too large models in the increasingly huge model spaces being considered in genomics and other fields. A popular replacement was to adopt a suggestion of Harold Jeffreys for the variable selection problem in which a total of $k$ possible variables are being considered for inclusion in the model: give the collection of all models containing $d$ variables ($d = 0, . . . , k$) prior probability $1/(k + 1)$ and then divide this prior probability equally among the models in the collection. Many other choices of model prior probabilities that impose severe parsimony have also been introduced. We begin by reviewing the problems with using equal model prior probabilities and then discuss some serious problems with the Jeffreys choice. Finally, we introduce and study a number of objective alternative choices of model prior probabilities, from both numerical and theoretical perspectives.

翻译：多年来，在贝叶斯模型不确定性分析中，默认使用等模型先验概率已是惯例。至少在二十年前，人们发现这种做法存在问题，它会导致在基因组学及其他领域中日益庞大的模型空间里，倾向于支持规模过大的模型。一种流行的替代方案是采用哈罗德·杰弗里针对变量选择问题提出的建议：当总共考虑 $k$ 个可能变量纳入模型时，赋予包含 $d$ 个变量（$d = 0, . . . , k$）的所有模型集合先验概率 $1/(k + 1)$，然后在该集合内等分这一先验概率。此外，许多其他施加严格简约性的模型先验概率选择也被提出。我们首先回顾使用等模型先验概率存在的问题，然后讨论杰弗里选择中的一些严重缺陷。最后，我们从数值和理论两个角度，提出并研究若干客观的模型先验概率替代方案。