We perform fully Bayesian inference for stochastic differential equation mixed-effects models (SDEMEMs) using data at discrete times that may be incomplete and subject to measurement error. SDEMEMs are flexible hierarchical models that are able to account for random variability inherent in the underlying time-dynamics, as well as the variability between experimental units and, optionally, account for measurement error. We consider inference for state-space SDEMEMs, however the inference problem is complicated by the typical intractability of the observed data likelihood which motivates the use of sampling-based approaches such as Markov chain Monte Carlo. Our proposed approach is the use of a Gibbs sampler to target the marginal posterior of all parameter values of interest. Our algorithm is made computationally efficient through careful use of blocking strategies and correlated pseudo-marginal Metropolis-Hastings steps within the Gibbs scheme. The resulting methodology is flexible and is able to deal with a large class of SDEMEMs. We demonstrate the methodology on state-space models describing two applications of increasing complexity and compare with alternative approaches. For these two applications, we found that our algorithm is about ten to forty times more efficient, depending on the considered application, than similar algorithms not using correlated particle filters.

中文翻译：

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使用相关粒子伪边际算法对随机微分方程混合效应模型进行有效推理

我们使用离散时间的数据对随机微分方程混合效应模型 (SDEMEMs) 执行完全贝叶斯推理，这些数据可能不完整并受测量误差影响。SDEMEMs 是灵活的分层模型，能够解释潜在时间动态中固有的随机可变性，以及实验单元之间的可变性，并可选地考虑测量误差。我们考虑对状态空间 SDEMEM 进行推理，但是由于观察到的数据似然的典型难以处理，推理问题变得复杂，这促使使用基于采样的方法，例如马尔可夫链蒙特卡罗。我们提出的方法是使用 Gibbs 采样器来定位所有感兴趣参数值的边缘后验。通过在 Gibbs 方案中仔细使用阻塞策略和相关的伪边际 Metropolis-Hastings 步骤，我们的算法在计算上变得高效。由此产生的方法是灵活的，能够处理一大类 SDEMEM。我们展示了描述两个日益复杂的应用程序的状态空间模型的方法，并与替代方法进行比较。对于这两个应用，我们发现我们的算法比不使用相关粒子滤波器的类似算法效率高出大约 10 到 40 倍，具体取决于所考虑的应用。我们展示了描述两个日益复杂的应用程序的状态空间模型的方法，并与替代方法进行比较。对于这两个应用，我们发现我们的算法比不使用相关粒子滤波器的类似算法效率高出大约 10 到 40 倍，具体取决于所考虑的应用。我们展示了描述两个日益复杂的应用程序的状态空间模型的方法，并与替代方法进行比较。对于这两个应用，我们发现我们的算法比不使用相关粒子滤波器的类似算法效率高出大约 10 到 40 倍，具体取决于所考虑的应用。