Stochastic differential equation mixed-effects models (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. Fully Bayesian inference for state-space SDEMEMs is performed, using data at discrete times that may be incomplete and subject to measurement error. 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. A Gibbs sampler is proposed to target the marginal posterior of all parameter values of interest. The 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. The methodology is demonstrated on three case studies, including tumor growth dynamics and neuronal data. The gains in terms of increased computational efficiency are model and data dependent, but unless bespoke sampling strategies requiring analytical derivations are possible for a given model, we generally observe an efficiency increase of one order of magnitude when using correlated particle methods together with our blocked-Gibbs strategy.
翻译:州空间SDEM模型(SDEMEMs)是灵活的等级模型,能够说明潜在时间动力中固有的随机变异性,以及实验单位之间的变异性,以及测量误差的可选性。对州空间SDEMs进行了完全的巴伊斯推论,在离散时使用的数据可能是不完整的,并可能发生测量误差。然而,观察到的数据可能性的典型易感性促使采用诸如Markov链 Monte Carlo等抽样方法的典型易感性使推论问题复杂化。建议以Gibs取样器为对象,针对所有感兴趣参数值的边际外缘标。算法是通过在Gibs系统中谨慎使用阻塞策略和相关的伪边际Meopolis-Hasing步骤进行计算效率的。由此产生的方法具有灵活性,能够处理大量的SDEMMs。三种案例研究,包括肿瘤生长动态和神经元数据,表明在提高计算效率方面的收益是建模和数据依赖的,但除非在一般情况下使用需要分析性战略的采样战略,从而可以使用一种测测测得的粒度提高效率的方法。