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: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=612573
• 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.

统计学有大量的程序，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;数据量可以从最少的几个到最少的几个。 真正的巨大。程序总是有目的的。所有认真的参与者都想知道程序完成或达到目的的程度如何。对于探索性使用，这意味着在日常校准的意义上对程序进行校准。为了验证它，至少在一定程度上，它意味着可重复性。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300万分之一的相对数。所有这些都涉及到某种程度的建模，以评估手术可能发生的情况。希格斯粒子的搜索本质上涉及泊松计数，我们的推理小组有助于提高分析的准确性，并从最初的双侧转换到所需的单侧置信度和检验程序。 该研究计划的重点是探索程序的校准和再现性的验证，所有这些都是在被调查对象的全部或部分建模的背景下进行的。我们之前已经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，对于一大类常规统计模型，在获取检验程序时所涉及的任意性现已被消除，此类模型的贝叶斯程序已得到澄清，Jeffreys关于事先信息的长期存在且有问题的建议已通过一个简单的程序调整而恢复，这在其可用性的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，在这种环境中，信息在空间和时间上进行本地组装，并且所产生的部分相关信息将被准确有效地组合。这个问题作为复合可能性出现，现在正在扩展到更重要的复合重要性，在大量数据的背景下有巨大的需求。 对于广泛的模型，众所周知，频率和贝叶斯对线性参数给出了非常等效的结果，但在参数曲率存在的情况下，结果会向相反的方向变化：由于频率分析是可重复的，这就直截了当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校正，使贝叶斯方法的便利性;该方法现在已经建立，我们的研究寻求广泛的实施。 指数模型的关键工具可以被检验到二阶而不是三阶。简化的模型，然后给出二阶程序很容易，接近三。这项技术将得到广泛的研究。