Proper Likelihoods for Bayesian Analysis
本文探讨了贝叶斯分析中似然函数的选择问题，提出后验概率有效性的新定义，并给出数值方法检验似然函数的适用性，对统计学者和数据分析师有参考价值。
The validity of posterior probability statements follows from probability calculus when the likelihood is the density of the observations. To investigate other cases, a second, more intuitive definition of validity is introduced, based on coverage of posterior sets. This notion of validity suggests that the likelihood must be the density of a statistic, not necessarily sufficient, for posterior probability statements to be valid. A convenient numerical method is proposed to invalidate the use of certain likelihoods for Bayesian analysis. Integrated, marginal, and conditional likelihoods, derived to avoid nuisance parameters, are also discussed.