Longevity-related Statistics and Their Perturbation Analysis: A Markov Chain, Matrix Calculus Approach

人类寿命一直是人口统计学研究的中心焦点。 它反映了从婴儿死亡率到老年死亡率以及介于两者之间的整个生命周期的死亡率的强度、年龄模式和原因。本研究项目的目标是开发和应用新的数学工具进行寿命的敏感性分析。敏感性分析量化了变化的影响，这些新工具将使研究人员能够量化死亡率变化对测量寿命的各种统计数据的影响。这些统计数据包括预期寿命、寿命变化指数以及特定死亡原因对这些统计数据的贡献。敏感性分析在寿命研究中很重要，因为在过去的两个世纪中，由于医学、公共卫生和技术的空前进步，人类死亡率发生了巨大变化。除了这些时间上的变化之外，在任何时候，各区域、国家和社会经济群体的寿命模式也各不相同。总之，寿命方面的这些变化对社会具有重要影响，决定了人口的年龄结构以及对医疗保健和社会服务的需求。在这项研究中开发的新的分析方法将广泛用于研究寿命的变化及其后果。

Human longevity has always been a central focus of demographic research. It reflects the intensity, age pattern, and causes of mortality throughout the life cycle, from infant mortality to old-age mortality and everything in between. The objective of this research project is to develop and apply new mathematical tools for the sensitivity analysis of longevity. Sensitivity analysis quantifies the effects of changes, and these new tools will enable researchers to quantify the effects of changes in mortality on various statistics measuring longevity. Those statistics include life expectancy, indices of variation in longevity, and the contributions of particular causes of death to those statistics.Sensitivity analysis is important in the study of longevity because human mortality has changed dramatically over the last two centuries, due to unprecedented advances in medicine, public health, and technology. In addition to these temporal changes, at any one time, patterns of longevity also differ among regions, countries, and socio-economic groups. Together, these changes in longevity have important implications for society, determining, as they do, the age structure of populations and the needs for medical care and social services. The new analytical methods developed in this research will be widely useful in studies of changing longevity and its consequences.