常微分方程模型的贝叶斯最优设计及其在生物科学中的应用
Bayesian optimal design for ordinary differential equation models with application in biological science
摘要：
贝叶斯最优设计被认为是响应分布取决于非线性常微分方程系统的解决方案的实验。动机是一个实验，以估计参数的方程管理的氨基酸通过细胞膜在人类胎盘的运输。这种非线性模型的决策理论贝叶斯实验设计在概念上是非常有吸引力的，允许正式纳入先验知识，以克服频率论设计的参数依赖性和不太依赖于渐近近似。然而，必要的近似和最大化，通常分析棘手的，预期效用的结果在计算上具有挑战性的问题。如果微分方程的解不能以封闭形式获得，则这些问题进一步加剧。本文提出了一种新的组合的概率解嵌入在一个蒙特卡罗近似的期望效用与循环下降的光滑近似找到最优设计的方程。一种新的预计算算法减少了计算负担，使搜索更大的问题的最佳设计可行。该方法被证明是通过寻找新的设计，一些常见的模型来自微分方程，并提供最佳的设计胎盘实验。
英文摘要：
Bayesian optimal design is considered for experiments where the response distribution depends on the solution to a system of non-linear ordinary differential equations. The motivation is an experiment to estimate parameters in the equations governing the transport of amino acids through cell membranes in human placentas. Decision-theoretic Bayesian design of experiments for such nonlinear models is conceptually very attractive, allowing the formal incorporation of prior knowledge to overcome the parameter dependence of frequentist design and being less reliant on asymptotic approximations. However, the necessary approximation and maximization of the, typically analytically intractable, expected utility results in a computationally challenging problem. These issues are further exacerbated if the solution to the differential equations is not available in closed-form. This paper proposes a new combination of a probabilistic solution to the equations embedded within a Monte Carlo approximation to the expected utility with cyclic descent of a smooth approximation to find the optimal design. A novel precomputation algorithm reduces the computational burden, making the search for an optimal design feasible for bigger problems. The methods are demonstrated by finding new designs for a number of common models derived from differential equations, and by providing optimal designs for the placenta experiment.
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