Statistical inference in actuarial, engineering, and life sciences

在精算、工程、生命和其他科学中，有许多关于序列、函数及其函数的悬而未决的问题。拟议的研究计划有两个相互交织的目标：A)创建和探索适当的统计模型并改进现有的模型，B)产生适当的统计推断理论，并在模拟研究和真实数据中对其进行测试。我特别感兴趣的具体问题涉及如下领域：1)对生物、电气和机械系统中的老化过程进行建模，应用于精算、生命和工程科学；2)统计可靠性工程，目的是确定和研究最优的老化、磨损、更换策略；3)开发测试，以区分确定性噪声和随机噪声，并应用于医学和电信。这些研究领域产生了最有趣的统计和概率问题，也给应用数学和纯数学带来了挑战。

There are numerous unresolved problems in actuarial, engineering, life and other sciences dealing with sequences, functions, and their functionals. The proposed research program has two intertwined objectives: A) creating and exploring appropriate statistical models and improving upon existing ones, and B) producing appropriate statistical inferential theories and testing them in simulation studies as well as on real data. Specific problems of my particular interest concern such areas as: 1) modeling ageing processes in biological, electrical, and mechanical systems with applications in actuarial, life, and engineering sciences, 2) statistical reliability engineering with the aim at determining and investigating optimal burn-in, wear-out, replacement policies, 3) developing tests for distinguishing deterministic noises from random ones with applications in medical sciences and telecommunications. These research areas give rise to most interesting statistical and probabilistic problems as well as to challenges in applied and pure mathematics.