基于元模型方法的复杂混合模型参数估计
Parametric estimation of complex mixed models based on meta-model approach
摘要：
复杂的生物过程通常是在一群个体中进行长期实验的。纵向数据，然后可用的统计挑战是更好地了解潜在的生物机制。标准的统计方法是混合效应模型，其回归函数现已高度发展，可精确描述生物过程（多维常微分方程或偏微分方程的解）。当没有解析解时，经典的估计方法依赖于EM算法（SAEM）的随机版本与MCMC算法的耦合。这个过程需要许多评估的回归函数，这显然是禁止时，一个耗时的求解器用于computingit.In这项工作中，提出了一个元模型依赖于一个高斯过程仿真器来代替这个回归函数。由于这种近似而产生的新的不确定性来源可以被纳入模型中，这导致了所谓的混合元模型。保证了对该混合元模型中的最大似然估计与用精确混合模型获得的最大似然估计之间的距离的控制。最后，通过数值模拟验证了该方法的有效性。
英文摘要：
Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The standard statistical approach is mixed-effects model, with regression functions that are now highly-developed to describe precisely the biological processes (solutions of multi-dimensional ordinary differential equations or of partial differential equation). When there is no analytical solution, a classical estimation approach relies on the coupling of a stochastic version of the EM algorithm (SAEM) with a MCMC algorithm. This procedure needs many evaluations of the regression function which is clearly prohibitive when a time-consuming solver is used for computing it. In this work a meta-model relying on a Gaussian process emulator is proposed to replace this regression function. The new source of uncertainty due to this approximation can be incorporated in the model which leads to what is called a mixed meta-model. A control on the distance between the maximum likelihood estimates in this mixed meta-model and the maximum likelihood estimates obtained with the exact mixed model is guaranteed. Eventually, numerical simulations are performed to illustrate the efficiency of this approach.
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