Yashin A I, Manton K G, Vaupel J W
Theor Popul Biol. 1985 Apr;27(2):154-75. doi: 10.1016/0040-5809(85)90008-5.
Various multivariate stochastic process models have been developed to represent human physiological aging and mortality. These efforts are extended by considering the effects of observed and unobserved state variables on the age trajectory of physiological parameters. This is done by deriving the Kolmogorov-Fokker-Planck equations describing the distribution of the unobserved state variables conditional on the history of the observed state variables. Given some assumptions, it is proved that the distribution is Gaussian. Strategies for estimating the parameters of the distribution are suggested based on an extension of the theory of Kalman filters to include systematic mortality selection. Various empirical applications of the model to studies of human aging and mortality as well as to other types of "failure" processes in heterogeneous populations are discussed.
已经开发了各种多元随机过程模型来表示人类生理衰老和死亡率。通过考虑观察到的和未观察到的状态变量对生理参数年龄轨迹的影响，这些工作得到了扩展。这是通过推导描述以观察到的状态变量历史为条件的未观察到的状态变量分布的柯尔莫哥洛夫-福克-普朗克方程来实现的。在给定一些假设的情况下，证明该分布是高斯分布。基于卡尔曼滤波器理论的扩展以纳入系统死亡率选择，提出了估计分布参数的策略。讨论了该模型在人类衰老和死亡率研究以及异质群体中其他类型“失效”过程研究中的各种实证应用。
