Bayes assisted model assessment

贝叶斯辅助模型评估

• 批准号: RGPIN-2021-03185
• 负责人: Lockhart, Richard
• 金额: $ 3.13万
• 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: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=765774
• 关键词: Bayes; assisted; model; assessment

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.

评估模型假设的问题有两个当前重要的特征。首先，统计学家继续开发无数新的临时程序。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无法核实的假设来解决的；这些假设通常用收敛率的语言来表达，因为参数的数量p随着样本大小的某种度量（比如n）而增长。高维模型和推理程序经常展示这两种情况。我正在从事一项长期计划，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性的影响。我特别关注模型评估和验证。我考虑的是对某些函数有假设的统计模型。在拟合优度（我的主要工作领域）中，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）或多变量分析（关于copula的假设）或时间序列（关于谱分布的假设）相关。我研究的主要目的是评估这些假设。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：我们将开发和评估建模假设的假设检验。我们的框架从某个函数的有限维参数说明开始。那么零假设要么是参数模型，要么是半参数规范，其中它是要检查的函数的参数规范。然后通过扩展空模型的无限维非参数模型指定备选方案。我们将先验放在备选方案上，寻求捕获合理备选方案的性质，然后描述和研究所得到的最优测试。先验被视为开发测试的工具，作为比较测试的工具，并且通过计算拒绝假设模型后验，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）先验条件会导致这种测试。我们需要对分布假设进行检验：关于数据分布的假设，或者关于回归模型中的误差的假设，或者关于潜在变量的假设（如脆弱性等随机效应）。我们将努力开发回归函数、链接函数、谱密度等的测试。更广泛地说，我希望使用先验来开发和评估多步骤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的粒子发现工作，以便将良好的频率理论特性与重要的信息先验结合起来。