高维随机微分混合效应模型的实用估计
Practical Estimation of High Dimensional Stochastic Differential Mixed-Effects Models
摘要：
随机微分方程（SDEs）是建立模型的工具，其动力学受随机噪声的影响的物理现象。通过估计一个随机变量的参数，可以识别系统在其漂移周围的内在随机性，并将其与漂移本身分离。当它是一个给定的人口内的动态模型的兴趣，即同时模拟几个实验或科目的性能，混合效应建模允许之间的区别和实验内的变异性。提出了一个框架，人口内的动态模型使用SDES，同时代表几个来源的变化：实验之间的变异性使用混合效应的方法和随机性在个人动态使用SDES。这些“随机微分混合效应模型”在例如药代动力学/药效学和生物医学建模中有应用。提出了一种参数估计方法，并给出了有效实现的计算准则。最后，该方法进行了评估，使用模拟从标准的模型，如二维Ornstein-Uhlenbeck（ORM）和平方根模型。
英文摘要：
Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified and separated from the drift itself. When it is of interest to model dynamics within a given population, i.e. to model simultaneously the performance of several experiments or subjects, mixed-effects modelling allows for the distinction of between and within experiment variability. A framework to model dynamics within a population using SDEs is proposed, representing simultaneously several sources of variation: variability between experiments using a mixed-effects approach and stochasticity in the individual dynamics using SDEs. These "stochastic differential mixed-effects models" have applications in e.g. pharmacokinetics/pharmacodynamics and biomedical modelling. A parameter estimation method is proposed and computational guidelines for an efficient implementation are given. Finally the method is evaluated using simulations from standard models like the two-dimensional Ornstein-Uhlenbeck (OU) and the square root models.
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