Bayes assisted frequentist model assessment and statistical inference

数据的统计分析通常要求分析师对数据的生成方式做出假设。我的研究主要是为了开发统计技术来检验这些假设。数据分析师所做的假设通常在很多方面都是错误的。因此，所建议的评估假设的许多方法都是临时的；它们侧重于假设可能出错的一个特定方向，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很合理，或者因为它们似乎适合进行数学分析。 在接下来的五年里，我将与我的学生和同事一起，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，然后尝试找到对于所选特定贝叶斯描述而言近似最佳的方法(技术上讲，对于给定的关于模型假设失败的性质的“先验分布”，最佳可能的方法)。这种原则性的方法留下了大量的工作要做，以评估产生的分析技术。在复杂的统计问题中，在选择贝叶斯先验描述方面有很大的灵活性，很难看出某个特定的选择是否隐藏了不合理的现实世界假设；为我们提出的特定建议评估这种危险将是我工作的重点之一。 另一个焦点将出现在这样一个事实上，即通常不可能找到在计算上可行的“最佳”程序；通常近似最佳是我们所能做的最好的。然后，我们需要评估近似的质量。 记住，一些特别程序运作得很好，这也是明智的。我工作的另一个重点将是评估此类程序离最佳可能的程序还有多远。通常，一个容易计算、近乎最佳的方法会比一个复杂、难以计算、可能的最佳解决方案更容易被接受。 除了示范评估领域的这项基本工作外，我还将在其他领域探讨各种问题。其中最重要的考虑是寻找新的物理，例如在欧洲核子研究中心寻找希格斯玻色子。这种特殊的搜索包括扫描一系列可能的质量以寻找寻找的粒子，并在每个质量上从统计学上寻找数据集的相关部分中的信号。目前这类搜索的策略是，如果统计证据足够压倒性，则宣布找到的粒子；如果没有发现，则遍历可能的质量范围，如果粒子确实存在，排除数据允许的尽可能多的质量，使其不可能成为真实质量的可能候选者。与学生们一起，我一直致力于并将致力于使用上面提到的贝叶斯思想，将这两个步骤结合成一个一步程序，以实现可能的最佳长期行为。

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.