Including prior information about model parameters is a fundamental step of any Bayesian statistical analysis. It is viewed positively by some as it allows, among others, to quantitatively incorporate expert opinion about model parameters. It is viewed negatively by others because it sets the stage for subjectivity in statistical analysis. Certainly, it creates problems when the inference is skewed due to a conflict with the data collected. According to the theory of conflict resolution (O'Hagan and Pericchi, 2012), a solution to such problems is to diminish the impact of conflicting prior information, yielding inference consistent with the data. This is typically achieved by using heavy-tailed priors. We study both theoretically and numerically the efficacy of such a solution in a regression framework where the prior information about the coefficients takes the form of a product of density functions with known location and scale parameters. We study functions with regularly varying tails (Student distributions), log-regularly-varying tails (as introduced in Desgagn\'e (2015)), and propose functions with slower tail decays that allow to resolve any conflict that can happen under that regression framework, contrarily to the two previous types of functions. The code to reproduce all numerical experiments is available online.

翻译：在模型参数中包含先验信息是任何贝叶斯统计分析的基本步骤。一些人对此持积极态度，因为它可以定量融入专家对模型参数的意见；另一些人则持负面看法，因为它为统计分析引入了主观性。当然，当推断因与收集到的数据存在冲突而产生偏差时，这会引发问题。根据冲突解决理论（O'Hagan and Pericchi, 2012），解决此类问题的方法是减少冲突先验信息的影响，使推断与数据保持一致。这通常通过使用重尾先验分布来实现。我们从理论和数值角度研究了这种解决方案在回归框架下的有效性，其中关于系数的先验信息以已知位置和尺度参数的密度函数乘积形式给出。我们研究了具有规则变化尾部（Student分布）和日志规则变化尾部（如Desgagné (2015) 所提出）的函数，并提出了尾部衰减更慢的函数，与前述两类函数不同，这些函数能够解决回归框架下可能发生的任何冲突。所有数值实验的复现代码均可在线获取。