Mathematical Sciences: Conditional and Unconditional Confidence

本研究探讨和解的无条件（前数据）的推理和条件（后数据）的推理使用的客观手段评估的条件效度的频率论信心。一般方法分配后数据的信心被认为是基于后验分布。由此产生的属性和频率有效性的后数据的置信估计进行检查。将研究正常均值和方差的体积减少置信集的后数据推断，其中可能以频率有效的方式实现较低的体积和连贯的后数据置信度。本文将研究离散分布的可容许非随机置信集的条件性质，目的是获得相干的频率有效的事后数据推断。

The research investigates reconciliation of unconditional (pre-data) inference and conditional (post-data) inference using an objective means of assessing conditional validity of frequentist confidence. General methods of assigning post-data confidence are considered which are based on posterior distributions. The resulting properties and frequentist validity of the post-data confidence estimator are examined. Post-data inference for volume-reducing confidence sets for normal means and variances is to be studied where it is possible to achieve lower volume and coherent post-data confidence in a frequency- valid way. The conditional properties of admissible nonrandomized confidence sets from discrete distributions will be investigated with the goal of obtaining coherent frequency-valid post-data inference.