Mathematical Sciences: Assessing Robustness of Inference

所有的统计过程都会导致一个推论，一个基于观察数据和假设模型的陈述。由于通常存在难以（或不可能）检查的模型假设，因此期望推断对模型假设具有鲁棒性。我们最关心的推理是置信集和假设检验的事后数据准确性度量。这些措施往往是通过决策理论或贝叶斯参数，因此是基于抽样分布，损失函数和先验分布的假设。在这里，我们想研究精度估计的性能，同时使用频率论和贝叶斯准则，因为基本的假设是放松的。我们最感兴趣的程序构造默认先验知识，这些往往表现良好的频率和贝叶斯审查。我们将解决抽样鲁棒性的一种方法是联合收割机将默认先验与经验似然相结合，以获得（某种程度上）自动推理鲁棒过程。推理的鲁棒性将使用各种标准来判断，例如后验概率的范围，多重和距离惩罚损失函数以及一种新的（有前途的）概率膨胀理论。

All statistical procedures result in an inference, a statement that is based on both the observed data and the assumed model. Since there are often model assumptions that are difficult (or impossible) to check, it is desirable for inferences to be robust against model assumptions. The inferences that we are most concerned about are post (data accuracy measures for confidence sets and hypothesis tests. Such measures are often derived through decision theoretic or Bayesian arguments, hence are based on assumptions about sampling distributions, loss functions, and prior distributions. Here we want to investigate the performance of accuracy estimators, using both frequentist and Bayesian criteria, as the underlying assumptions are relaxed. We are most interested in procedures constructed from default priors, for these tend to perform well under both frequentist and Bayesian scrutiny. One way that we will address the sampling robustness is to combine the default priors with an empirical likelihood to obtain a (somewhat) automatic inference robust procedure. Robustness of inference will be judged using a variety of criteria such as ranges of posterior probabilities, multiple and distance penalizing loss functions and a new (and promising) theory of dilation of probabilities.