Reproducible Bayes, Higher order likelihood and Inference methodology

统计学有丰富的程序，从记录平均收集的数据，到检查药物的实验结果，再到最近寻找希格斯玻色子所需的验证；数据量从最少的几个到*真正的大量不等。选择一个程序总是有一些目的的。所有认真的参与者都想知道这些程序完成或达到目的的程度如何。对于探索性使用，这意味着程序的校准，在日常的校准意义上。而要验证这一点，至少在一定程度上意味着可重复性。对于一些校准，这可能相当于熟悉的20分中的19分：而对于一些验证，这可能涉及到3万分之一的相反情况。所有这一切都涉及到一定程度的建模，以评估一个程序可能会发生什么。希格斯搜索本质上涉及泊松计数，我们的推理组有助于提高分析的准确性，并从最初的双面转向所需的单边置信度和测试程序。*本研究计划侧重于探索性程序的校准和重复性的验证，所有这些都是在对被调查对象进行完整或部分建模的背景下进行的。我们以前已经制定了高度准确的评估程序，并调查了正在使用的统计论点。特别是，对于一大类常规统计模型来说，获取测试程序所涉及的任意性现已消除，这类模型的贝叶斯程序已得到澄清，杰弗里斯关于先验信息的长期和有问题的提议也没有通过一项简单的程序调整恢复，这在其问世的65年中是没有预见到的。该研究计划还将这一点扩大到大数据环境，在这些环境中，信息在空间和时间上进行本地组装，并确保由此产生的部分依赖的数据信息能够准确而高效地组合在一起。这个问题是以复合似然的形式出现的，现在正被扩展到更重要的复合意义上，在大到大量数据的背景下具有巨大的需求。*对于广泛的模型，众所周知，对于线性参数，频率和贝叶斯给出了几乎相同的结果，但在参数曲率存在的情况下，频率和贝叶斯给出了相反的方向：由于频率分析是可重现的，这直截了当地表明贝叶斯通常是不可重现的。研究计划正在寻求对此进行修正的广泛背景实施，以允许贝叶斯方法的更大便利性；方法论现在已经确立，我们的研究寻求广泛实施。*指数模型的关键工具可以被检验到二阶而不是三阶。然后，简化的模型很容易给出第二个程序，接近第三个程序。这项技术将得到广泛的检验。**

Statistics has a wealth of procedures that range from recording an average of collected data, to examining the experimental results on a drug, to the verifying that is needed in the recent search for the Higgs Boson; the amount of data can range from some minimal few to the***truly massive. There is always some purpose for  a procedure. And all serious participants would want to know how well the procedures accomplished or achieved the purpose. For an exploratory use this means calibration of the procedure, in the every day sense of calibration. And for verifying it means, in part at least, reproducibility. For some calibration this might amount to the familiar 19 out of 20: and for some verification it could involve 1 in 3 million for some opposite. All of this involves some level of modelling to assess what can happen with a procedure. The Higgs search  intrinsically involved Poisson counts and our inference group was instrumental in promoting higher accuracy for that analysis, and switching to the needed one-sided confidence and testing procedures from the initial two-sided.***This research program is  focused on the calibration of exploratory procedures and the verification of reproducibility, all in the context of full or partial modelling of the  object under investigation. We have previously developed highly accurate assessment procedures and investigated the statistical arguments being used. In particular the arbitrariness involved in obtaining testing procedures has now been removed for a broad class of regular statistical models, and the Bayesian procedures for such models have been clarified and a long standing and problematic proposal by Jeffreys for prior information has  been reinstated by a simple procedural adjustment that had not been foreseen in the 65 years of its availability. The research program  also broadens this to the large data contexts where information is assembled locally in space and time and convenience, and  the resulting pieces of partially dependent  information are to be combined accurately and efficiently. This issue arose as composite likelihood and is now  being extended to the more important composite significance with huge needs in the context of large to massive data.***For a wide range of models it is known that frequency and Bayes give closely equivalent results for linear parameters but then change in opposite directions in the presence of parameter curvature: as the frequency analysis is reproducible this says bluntly that the Bayes is usually not reproducible. The research program is seeking a broad context implementation of corrections for this, to allow  the  convenience of the Bayes approach; the methodology is now  established and our research seeks wide implementation.*** The key tool of exponential models can be examined to second rather than third order. The simplified model then gives  second order procedures easily, close to  third. This technique will be examined widely.**