Likelihood estimation for stochastic differential equations with mixed effects
混合效应随机微分方程的似然估计AI 解读 ↓
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混合效应随机微分方程的似然估计
- 研究问题
- 当多个实验单位的动态过程具有随机参数且仅被离散观测时，如何开展似然估计，同时描述过程噪声与单位之间的异质性？
- 方法与思路
- 作者通过模拟扩散桥增广数据，构造 Gibbs 采样器与随机 EM 算法，并讨论测量误差扩展及指数族扩散过程下的算法简化。
- 材料陈述的贡献
- 摘要称，所用扩散桥方法易实现且无需调参，计算时间随观测间隔线性增长；模拟展示两类混合效应扩散模型的估计，并应用于神经元数据。
- 阅读关注点
- 应核对扩散桥模拟与似然近似的关系、随机效应分布、算法收敛条件，以及低采样频率和测量误差下的计算与估计表现。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收均未核实；摘要未说明完整模型条件、离散化误差或收敛诊断，模拟表现不能视为普遍保证。
原文摘要
Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the parameters vary between the individual experimental units, which has motivated a considerable interest in stochastic differential equations with mixed effects, where a subset of the parameters are random. These models enable simultaneous representation of randomness in the dynamics and variability between experimental units. When the data are observations at discrete time points, the likelihood function is only rarely explicitly available, so for likelihood-based inference to be feasible, numerical methods are needed. We present Gibbs samplers and stochastic EM-algorithms based on augmented data obtained by the simple method for simulation of diffusion bridges in Bladt and Sørensen (2014). This method is easy to implement and has no tuning parameters. The method is, moreover, computationally efficient at low sampling frequencies because the computing time increases linearly with the time between observations. The algorithms can be extended to models with measurement errors. The Gibbs sampler as well as the EM-algorithm are shown to simplify considerably for exponential families of diffusion processes, including many models used in practice. In a simulation study, the estimation methods are shown to work well for Ornstein-Uhlenbeck processes and t-diffusions with mixed effects. Finally, the Gibbs sampler is applied to neuronal data.