Mathematical Sciences: New Methodology for Predictive Inference

一个非参数的方法来选择模型的分类和生存数据，以期帮助启发的预测和预后因素。提出的测试采取的形式的中心极限定理的归一化评分功能。考虑到数据收集的顺序方面。研究的目标是为这些诊断建立良好的理论基础，并证明其实用性。对于生存模型，还将研究在充分统计条件下概率积分变换残差的分布特性。在这些属性很容易表征的情况下，将寻求条件，在该条件下，转换的顺序应用导致模型的预测有效性的测试。 基于结构化先验的经验贝叶斯置信区间的构建是在一个预测框架中进行的，将通过分析方法和自助样本来解决。比较几个验证标准将区分现有的和拟议的技术。聚焦于可观测量，将研究基于经验贝叶斯分布的预测区间的特性。 提出了一种新的分类和生存数据选择模型的方法。这种方法将有助于引出预测因子和预后因素。考虑到数据收集的顺序方面。研究的目标是为这些诊断建立良好的理论基础，并证明其实用性。在预测框架中基于结构化先验的经验贝叶斯置信区间的构建。这些区间的构建将通过分析方法和bootstrap样本来解决。比较几个验证标准将区分现有的和拟议的技术。 以观测量为重点，将研究基于经验贝叶斯分布的预测区间的特性。

A non-parametric approach is developed to select models for categorical and survival data, with a view to helping the elicitation of predictors and prognostic factors. The tests put forward take the form of central limit theorems for normalized scoring functions. The sequential aspect of the data collection is taken into account. The goal of the research is to establish sound theoretical foundations for these diagnostics and to demonstrate their practicality. For survival models, the distributional properties of residuals from the probability integral transform conditional on sufficient statistics will also be studied. In the event that these properties are easily characterized, conditions, under which a sequential application of the transformation leads to a test of predictive validity of the model, will be sought. The construction of empirical Bayes confidence intervals based on structured priors is set in a predictive framework and will be addressed via both analytical methods and bootstrap samples. Comparison with respect to several validation criteria will discriminate between existing and proposed techniques. Focussing on observables, the characteristics of prediction intervals based on empirical Bayes distributions will be looked into. A novel approach for the selection models for categorical and survival data, is developed. This methodology will help in the elicitation of predictors and prognostic factors. The sequential aspect of the data collection is taken into account. The goal of the research is to establish sound theoretical foundations for these diagnostics and to demonstrate their practicality. The construction of empirical Bayes confidence intervals based on structured priors in a predictive framework. The construction of these intervals will be addressed via both analytical methods and bootstrap samples. Comparison with respect to several validation criteria will discriminate between existing and proposed techniques. Focussing on observables, t he characteristics of prediction intervals based on empirical Bayes distributions will be looked into.