Matching priors in principle provide a possible compromise between frequentist and Bayesian and default priors for routine use in Bayesian inference in that posterior probability of the parameter also provides an interpretation as confidence statements. Here we introduce a matching prior for the ratio of two log-normal means which is nontrivial because the derivation of matching prior requires the elicitation of a suitable orthogonal parameterization on the nuisance parameters and the computation of the marginal posterior distribution requires multidimensional integration over the nuisance parameter. Numerical integrations and approximation techniques could be used but they are difficult to use in general. Thus, we derive a matching prior based on a modification of the profile likelihood to avoid the elicitation of priors for the entire parameter and integration on the nuisance parameter. The proposed method is illustrated by real data examples and simulation studies under several configurations.

中文翻译：

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使用修正的轮廓似然法对两个对数正态平均值的比率进行客观贝叶斯分析

原则上，匹配先验会在频率和贝叶斯和贝叶斯推理中的常规使用默认先验之间提供折衷，因为该参数的后验概率还提供了对置信度的解释。在这里，我们为两个对数正态平均值之比引入了一个先验匹配，这是不平凡的，因为先验匹配的推导需要对扰民参数进行合适的正交参数化，而边际后验分布的计算则需要对扰民进行多维积分参数。可以使用数值积分和逼近技术，但通常很难使用它们。从而，我们基于轮廓似然的修改得出匹配的先验，以避免整个参数的先验和对扰动参数的积分。通过实际数据示例和几种配置下的仿真研究说明了该方法。