We propose a multivariate GARCH model for non‐stationary health time series by modifying the observation‐level variance of the standard state space model. The proposed model provides an intuitive and novel way of dealing with heteroskedastic data using the conditional nature of state‐space models. We follow the Bayesian paradigm to perform the inference procedure. In particular, we use Markov chain Monte Carlo methods to obtain samples from the resultant posterior distribution. We use the forward filtering backward sampling algorithm to efficiently obtain samples from the posterior distribution of the latent state. The proposed model also handles missing data in a fully Bayesian fashion. We validate our model on synthetic data and analyze a data set obtained from an intensive care unit in a Montreal hospital and the MIMIC dataset. We further show that our proposed models offer better performance, in terms of WAIC than standard state space models. The proposed model provides a new way to model multivariate heteroskedastic non‐stationary time series data. Model comparison can then be easily performed using the WAIC.

中文翻译：

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多变量重症监护数据的贝叶斯非平稳异方差时间序列模型


我们通过修改标准状态空间模型的观测水平方差，提出了一种用于非平稳健康时间序列的多元 GARCH 模型。所提出的模型提供了一种利用状态空间模型的条件性质来处理异方差数据的直观且新颖的方法。我们遵循贝叶斯范式来执行推理过程。特别是，我们使用马尔可夫链蒙特卡罗方法从所得后验分布中获取样本。我们使用前向过滤后向采样算法来有效地从潜在状态的后验分布中获取样本。所提出的模型还以完全贝叶斯方式处理缺失数据。我们在合成数据上验证了我们的模型，并分析了从蒙特利尔医院重症监护室获得的数据集和 MIMIC 数据集。我们进一步表明，就 WAIC 而言，我们提出的模型比标准状态空间模型提供了更好的性能。所提出的模型提供了一种对多元异方差非平稳时间序列数据进行建模的新方法。然后可以使用 WAIC 轻松执行模型比较。