Reproducible Bayes, Higher order likelihood and Inference methodology

可重现的贝叶斯、高阶似然和推理方法

• 批准号: RGPIN-2015-03794
• 负责人: Fraser, Donald
• 金额: $ 2.62万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=686796
• 关键词: Reproducible; Bayes; Higher; order; likelihood

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.**

统计学有丰富的程序，从记录收集到的数据的平均值，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；数据量的范围可以从极少的数据到巨大的数据量。程序总是有某种目的的。所有认真的参与者都想知道程序完成或达到目的的效果如何。对于探索性用途，这意味着对程序进行校准，即日常意义上的校准。对于验证来说，至少在某种程度上，它意味着可重复性。对于某些校准来说，这可能相当于我们熟悉的 20 分之 19：而对于某些验证来说，对于某些相反的情况，这可能涉及 300 万分之一。所有这些都涉及一定程度的建模来评估程序可能发生的情况。希格斯玻色子搜索本质上涉及泊松计数，我们的推理小组有助于提高该分析的准确性，并从最初的双面转换到所需的单面置信度和测试程序。***该研究计划的重点是探索性程序的校准和再现性的验证，所有这些都是在对所研究的对象进行完整或部分建模的背景下进行的。我们之前开发了高度准确的评估程序并调查了所使用的统计参数。特别是，对于一类广泛的常规统计模型，获取测试程序所涉及的任意性现已被消除，此类模型的贝叶斯程序也已得到澄清，杰弗里斯关于先验信息的长期存在且有问题的提议已通过简单的程序调整得到恢复，而这一调整在其可用性 65 年中是没有预见到的。该研究计划还将其扩展到大数据环境，其中信息在空间、时间和便利性上进行本地组装，并且所得到的部分依赖的信息将被准确有效地组合。这个问题是作为复合似然性出现的，现在正在扩展到更重要的复合重要性，在大数据到海量数据的背景下具有巨大的需求。***对于各种模型，众所周知，频率和贝叶斯对于线性参数给出了完全相同的结果，但在参数曲率存在的情况下却在相反的方向上发生变化：由于频率分析是可再现的，这直接表明贝叶斯通常是不可再现的。该研究计划正在寻求对此进行更广泛的纠正，以方便使用贝叶斯方法；该方法现已建立，我们的研究寻求广泛实施。*** 指数模型的关键工具可以进行二阶而不是三阶检验。然后，简化模型可以轻松给出二阶过程，接近三阶过程。这项技术将得到广泛研究。**