On Comparing Asset Pricing Models
指出Barillas和Shanken（2018）提出的贝叶斯边际似然模型比较方法存在缺陷，因其使用的Jeffreys先验不满足密度变换性质，并通过模拟验证其表现不佳；作者提出一类新的不当先验，能产生有效的边际似然，从而可靠地识别资产定价模型中的风险因子。
ABSTRACT Revisiting the framework of (Barillas, Francisco, and Jay Shanken, 2018, Comparing asset pricing models, The Journal of Finance 73, 715–754). BS henceforth, we show that the Bayesian marginal likelihood‐based model comparison method in that paper is unsound : the priors on the nuisance parameters across models must satisfy a change of variable property for densities that is violated by the Jeffreys priors used in the BS method. Extensive simulation exercises confirm that the BS method performs unsatisfactorily. We derive a new class of improper priors on the nuisance parameters, starting from a single improper prior , which leads to valid marginal likelihoods and model comparisons. The performance of our marginal likelihoods is significantly better, allowing for reliable Bayesian work on which factors are risk factors in asset pricing models.