Bayes assisted frequentist model assessment and statistical inference

数据的统计分析通常要求分析人员对数据的生成方式做出假设。 我的研究主要是针对发展统计技术来检查这些假设。 数据分析师做出的假设通常在许多方面都是错误的。 因此，为评估假设而提出的许多方法都是临时性的;它们集中在假设可能错误的一个特定方向上，并提出了一些方法来检测偏离该特定方向的假设。 这些方法本身之所以被提出来，主要是因为它们听起来很合理，或者是因为它们似乎适合于数学分析。 在接下来的五年里，我将和我的学生和同事们一起，努力使这些特别的方法系统化。 我将使用所谓的贝叶斯辅助方法来描述偏离假设的可能方向，然后尝试找到近似最适合所选特定贝叶斯描述的方法（用专业术语来说，最适合给定的“先验分布”，即模型假设失效的性质）。 这种原则性的方法留下了许多工作要做，以评估所产生的分析技术。 在复杂的统计问题中，贝叶斯先验描述的选择有很大的灵活性，很难看出一个特定的选择是否埋下了不合理的真实的世界假设;对我们提出的特定建议的这种危险的评估将是我的工作重点之一。 另一个焦点将来自于这样一个事实，即通常不可能找到一个计算上可行的“最佳”程序;通常近似最佳是我们所能做的。 然后，我们需要评估近似的质量。 还应明智地记住，有些临时程序运作得很好。 我工作的另一个重点将是评估这种程序离最好的可能性还有多远。 通常，一个容易计算的、接近最佳的方法会比一个复杂的、难以计算的、可能的最佳解决方案更容易被接受。 除了模型评估领域的这一基本工作之外，我还将在其他领域研究各种问题。 其中最重要的是考虑寻找新的物理学，如在欧洲核子研究中心寻找希格斯玻色子。 这种特殊的搜索涉及扫描所寻找的粒子的可能质量范围，并在每个质量上从统计学上寻找数据集中相关部分的信号。 如果统计学证据足够充分，那么目前的这种搜索策略要么宣布发现了粒子，要么，如果没有发现粒子，那么，如果粒子确实存在，那么，在可能的质量范围内排除数据允许的尽可能多的质量，使其成为真实质量的可能候选者。 我一直在和学生们一起，并将继续使用上面提到的贝叶斯思想，将这两个步骤联合收割机结合成一个步骤，以实现最佳的长期行为。

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.