An Alternative to the Standard Bayesian Procedure for Discrimination Between Normal Linear Models
研究发现标准贝叶斯判别方法在中等样本量下会低估正确模型的后验概率，甚至在大样本下也不一致，原因是它高估了信息增益最小的模型；本文提出一种基于信息增益的修正方法，并证明其避免了林德利悖论。
We consider the standard Bayesian procedure for discrimination, focusing on its tendency to give low posterior probabilities to some correct models, even in conditions of moderate to large sampling sizes. Furthermore, in some situations that could well occur in practice, the standard procedure is even asymptotically inconsistent. We claim that the explanation is that the standard procedure inflates the posterior probability of the model that has the smallest expected increase in information about its parameters. We then propose to modify it by an amount related to the expected gain in information, and show that the 'Lindley paradox' does not occur. Finally, we obtain the limiting alternative criterion that results by letting the prior densities become noninformative, which enables us to measure how sensitive the discrimation is to the informative prior densities used.