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: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=651104
• 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.**

统计具有丰富的程序，从记录收集数据的平均值，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；数据量的范围可以很小，也可以非常大。程序总是有目的的。所有认真的参与者都想知道这些程序是如何完成或达到目的的。对于探索性使用，这意味着程序的校准，在日常意义上的校准。为了验证它，至少在一定程度上意味着再现性。对于某些校准，这可能相当于熟悉的20分之19；对于某些验证，它可能涉及300万分之一。所有这些都涉及到某种程度的建模，以评估一个过程可能发生的情况。希格斯粒子的搜索本质上涉及泊松计数，我们的推理小组在提高分析的准确性方面发挥了重要作用，并从最初的双边分析转向了所需的单边置信度和测试程序。***本研究计划的重点是在研究对象的全部或部分建模的背景下，对探索性程序的校准和可重复性的验证。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据。特别是，对于一大类常规统计模型，获得测试程序所涉及的随意性现在已经被消除，这些模型的贝叶斯程序已经得到澄清，Jeffreys关于先验信息的长期存在的有问题的建议已经通过简单的程序调整得到恢复，这在65年的可用性中是没有预见到的。该研究项目还将其扩展到大数据环境中，在大数据环境中，信息在空间和时间上是局部组装的，并且方便，并且由此产生的部分依赖信息片段要准确有效地组合在一起。这个问题是作为复合可能性而产生的，现在正被扩展到更重要的复合意义，在大数据到海量数据的背景下有着巨大的需求。***对于广泛的模型，已知频率和贝叶斯给出线性参数的近似等效结果，但随后在参数曲率存在的情况下发生相反方向的变化：由于频率分析是可重复的，这直言不讳地说贝叶斯通常是不可重复的。该研究计划正在寻求一个广泛的背景下实施更正，以允许贝叶斯方法的便利性；该方法现已确立，我们的研究寻求广泛实施。***指数模型的关键工具可以检验到二阶而不是三阶。简化后的模型容易得到二阶过程，接近于三阶过程。这项技术将被广泛研究