Ordinary differential equations (ODEs) are widely used for elucidating dynamic processes in various fields. One of the applications of ODEs is to describe dynamics of gene regulatory networks (GRNs), which is a critical step in understanding disease mechanisms. However, estimation of ODE models for GRNs is challenging because of inflexibility of the model and noisy data with complex error structures such as heteroscedasticity, correlations between genes, and time dependency. In addition, either a likelihood or Bayesian approach is commonly used for estimation of ODE models, but both approaches have benefits and drawbacks in their own right. Data cloning is a maximum likelihood (ML) estimation method through the Bayesian framework. Since it works in the Bayesian framework, it is free from local optimum problems that are common drawbacks of ML methods. Also, its inference is invariant for the selection of prior distributions, which is a major issue in Bayesian methods. This study proposes an estimation method of ODE models for GRNs through data cloning. The proposed method is demonstrated through simulation and it is applied to real gene expression time-course data.

中文翻译：

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通过数据克隆估计基因调控网络的常微分方程模型。

常微分方程 (ODE) 广泛用于阐明各个领域的动态过程。ODE 的应用之一是描述基因调控网络 (GRN) 的动态，这是理解疾病机制的关键步骤。然而，由于模型的不灵活性和具有复杂误差结构（例如异方差性、基因之间的相关性和时间依赖性）的噪声数据，GRN 的 ODE 模型的估计具有挑战性。此外，似然法或贝叶斯法通常用于 ODE 模型的估计，但这两种方法各有优缺点。数据克隆是通过贝叶斯框架的最大似然（ML）估计方法。由于它在贝叶斯框架中工作，它没有 ML 方法常见缺点的局部最优问题。此外，它的推论对于先验分布的选择是不变的，这是贝叶斯方法中的一个主要问题。本研究提出了一种通过数据克隆对 GRN 进行 ODE 模型估计的方法。所提出的方法通过仿真进行了论证，并将其应用于真实的基因表达时程数据。