Default Bayes Factors for Nonnested Hypothesis Testing
研究了非嵌套假设检验中几种默认贝叶斯因子（如分数贝叶斯因子、中位内在贝叶斯因子等）的性质，并与p值比较，适用于需要选择贝叶斯方法的统计或计量研究者。
Abstract Bayesian hypothesis testing for nonnested hypotheses is studied, using various “default” Bayes factors, such as the fractional Bayes factor, the median intrinsic Bayes factor, and the encompassing and expected intrinsic Bayes factors. The different default methods are first compared with each other and with the p value in normal one-sided testing, to illustrate the basic issues. General results for one-sided testing in location and scale models are then presented. The default Bayes factors are also studied for specific models involving multiple hypotheses. In particular, a multiple hypothesis testing example involving a sequential clinical trial is discussed. In most of the examples presented we also derive the intrinsic prior; this is the prior distribution, which, if used directly, would yield answers (asymptotically) equivalent to those for the given default Bayes factor.