Bayes assisted frequentist model assessment and statistical inference

贝叶斯辅助频率模型评估和统计推断

• 批准号: RGPIN-2014-06099
• 负责人: Lockhart, Richard
• 金额: $ 2.04万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=708308
• 关键词: Bayes; assisted; frequentist; model; assessment

Statistical analysis of data generally requires the analyst to make assumptions about the way the data were generated. My research is largely directed towards developing statistical techniques to check these assumptions. The assumptions data analysts make can generally be wrong in many ways. As a result many of the methods that have been suggested for assessing the assumptions have been ad hoc; they have focused on one particular direction in which the assumptions might be wrong and suggested some method for detecting departures from assumptions in that particular direction. The methods themselves are suggested largely because they sound reasonable or because they seem to lend themselves to mathematical analysis. In the next five years I, with my students and colleagues, will be trying to systematize these ad hoc approaches. I will use so-called Bayesian assisted approaches to describe the possible directions of departure from the assumptions and then try to find methods that are approximately the best possible for the particular Bayesian description chosen (in technical words, best possible for a given "prior distribution" on the nature of the failure of the model assumptions). Such a principled approach leaves much work to be done to evaluate the resulting analysis techniques. In complex statistical problems there is a great deal of flexibility in the choice of the Bayesian prior description and it can be hard to see whether or not a particular choice has buried within it unreasonable real world assumptions; evaluation of this danger for the particular suggestions we make will be one focus of my work. Another focus will arise from the fact that it will usually not be possible to find a computationally feasible "best" procedure; usually approximately best is as good as we can do. We then need to evaluate the quality of the approximation. It is also sensible to remember that some of the ad hoc procedures work very well. A further focus of my work will be to evaluate how far short of best possible such procedures lie. Often an easily computable, nearly best, method will be more happily received than a complex, hard to compute, best possible solution. In addition to this basic work in the area of model assessment, I will be pursuing a variety of problems in other areas. The most important of these considers searches for new physics such as the search for the Higgs boson at CERN. This particular search involved scanning a range of possible masses for the sought-for particle and at each mass looking, statistically, for a signal in the relevant part of a data set. The current strategy for searches of this kind then either declares the particle found, if the statistical evidence is sufficiently overwhelming or, if it is not found, runs through the range of possible masses excluding as many masses as the data permit from being possible candidates of the true mass if the particle really does exist. With students I have been, and will be, working on using the Bayesian ideas mentioned above to combine these two steps into a one-step procedure that achieves the best possible long run behaviour.

数据的统计分析通常要求分析人员对数据产生的方式做出假设。我的研究主要是为了开发统计技术来检验这些假设。数据分析师做出的假设通常在很多方面都是错误的。因此，许多评估假设的建议方法都是临时的；他们专注于一个特定的方向，在这个方向上假设可能是错误的，并提出了一些方法来检测在该特定方向上偏离假设的情况。这些方法本身之所以被提出，很大程度上是因为它们听起来合理，或者因为它们似乎适合于数学分析。