Bayes assisted model assessment

评估模型假设的问题有两个当前重要的特点。首先，统计学家继续开发无数新的特别程序。其次，我们越来越多地使用无法识别的模型。由此产生的困难是通过做出不可检验的假设来处理的；这些假设通常是以收敛速度的语言表述的，因为参数的数量p随着样本大小的某种度量而增长，比如n。高维模型和推理程序通常都能证明这两种情况。我参与了一个长期计划，试图减少程序只有这种特殊动机的程度，并从实际角度理解不可识别的影响。我特别关注模型评估和验证。我考虑的是统计模型，在这些模型中有关于某些函数的假设。在我的主要工作领域--拟合度方面，这些假设是关于分布函数或密度的，但这些想法也与回归模型(回归函数)、多变量分析(关于Copula的假设)或时间序列(关于谱分布的假设)相关。我的研究的主旨是评估这些假设。我目前的目标是使用贝叶斯思想来发现和评估频率测试。拟议研究计划的目标：我们将开发和评估模拟假设的假设检验。我们的框架从某些函数的有限维参数规范开始。然后，零假设是参数模型或半参数规范，其中它是要检查的功能的参数规范。然后，通过扩展零模型的无限维非参数模型来指定备选方案。我们将优先级放在备选方案上，试图捕捉合理备选方案的性质，然后描述和研究所产生的最优测试。先验被视为开发测试的工具，作为比较测试的工具，并通过计算假设模型被拒绝后的后验作为如何修改模型的指南。我们将尝试使用这些工具来研究众所周知的测试，以期了解什么(如果有的话)会导致这种测试。我们希望对分布假设进行检验：关于数据分布的假设，或回归模型中误差的假设，或潜在变量(如脆弱性等随机影响)的假设。我们将致力于开发回归函数、链接函数、谱密度等测试。更广泛地说，我希望使用先验经验来开发和评估多步推理过程的频率程序。我们还致力于将先验分布应用于更小的问题，如开关实验，在更简单的框架中复制我们在高能物理中发现粒子的工作，以便将良好的频率理论属性与非常有用的先验结合起来。

The problem of assessing model assumptions has two features of current importance. First, statisticians continue to develop myriad new ad hoc procedures. Second we are making more and more use of unidentifiable models. The resulting difficulties are handled by making uncheckable assumptions; these assumptions are often couched in the language of rates of convergence as the number of parameters, p, grows with some measure of sample size, say n. High dimensional models and inference procedures often showcase both. I am engaged in a long term program to try to reduce the extent to which procedures have only such ad hoc motivations and to understand in practical terms the impact of the non-identifiability. I am particularly focussed on model assessment and validation. I consider statistical models in which there are assumptions about some function. In goodness-of-fit, my main area of work, these assumptions are about distribution functions or densities but the ideas are also relevant to regression models (the regression function) or multivariate analysis (assumptions about a copula) or time series (assumptions about a spectral distribution). The main thrust of my research is then to assess the assumptions. My current goal is to use Bayesian ideas to find and evaluate frequentist tests. Objectives of the proposed research program: we will be developing and assessing hypothesis tests of modelling assumptions. Our framework starts with a finite dimensional parametric specification for some function. The null hypothesis is then either a parametric model or a semi-parametric specification in which it is the parametric specification of the function which is to be checked. The alternative is then specified via an infinite dimensional nonparametric model extending the null model. We put priors on the alternative seeking to capture the nature of reasonable alternatives, then describe and study the resulting optimal tests. The priors are treated as a tool in developing the test, as a tool in comparing tests and, by computing posteriors after rejection of the hypothesized model, as a guide to how to modify the model. We will be trying to use these tools to study well known tests with a view to learning what, if any, priors would lead to such tests. We want tests for distributional assumptions: assumptions about the distribution of the data, or of the errors in a regression model or for latent variables (random effects such as frailties). We will work to develop tests for regression functions, for link functions, for spectral densities, and many more such. More broadly still I hope to use priors to develop and evaluate frequentist procedures for multistep inferential processes. We are also working on applying prior distributions in much smaller problems such as on-off experiments, replicating our work on particle discovery in high energy physics in a much simpler framework in order to combine good frequency theory properties with seriously informative priors.