A Framework for Bayesian and Likelihood Approximations in Statistics
本文提出了一个统一框架，研究贝叶斯和频率学派近似方法，通过非平滑论证揭示高阶似然近似与贝叶斯近似的联系，并阐明两者关系，对依赖数据模型和非规则问题有指导意义。
Regular Bayesian and frequentist approximations in statistics are studied within a unified framework. In particular it is shown how some higher-order likelihood-based approximations arise from their Bayesian counterparts via an unsmoothing argument. This approach serves to shed new light on these formulae and to clarify relationships between Bayesian and frequentist inferences. For example, Bayesian interpretations of higher-order approximations can give insights into the acceptability, or otherwise, of these approximations from the point of view of ‘relevance’ to the actual data observed. Furthermore, this approach is a very natural one for the study of more general ‘nonregular’ problems, models for dependent data, and approximate conditional inference. For ease of exposition the development is in terms of a single real parameter. The main analytic development proceeds in terms of signed roots of log-density ratios.