Title: Bayesian Multivariate Nonlinear State Space Copula Models Show Chinese title

Title: 贝叶斯多元非线性状态空间copula模型

Abstract: In this paper we propose a flexible class of multivariate nonlinear non-Gaussian state space models, based on copulas. More precisely, we assume that the observation equation and the state equation are defined by copula families that are not necessarily equal. For each time point, the resulting model can be described by a C-vine copula truncated after the first tree, where the root node is represented by the latent state. Inference is performed within the Bayesian framework, using the Hamiltonian Monte Carlo method, where a further D-vine truncated after the first tree is used as prior distribution to capture the temporal dependence in the latent states. Simulation studies show that the proposed copula-based approach is extremely flexible, since it is able to describe a wide range of dependence structures and, at the same time, allows us to deal with missing data. The application to atmospheric pollutant measurement data shows that our approach is suitable for accurate modeling and prediction of data dynamics in the presence of missing values. Comparison to a Gaussian linear state space model and to Bayesian additive regression trees shows the superior performance of the proposed model with respect to predictive accuracy. Show Chinese abstract

Abstract: 本文提出了一类基于copula的灵活多元非线性非高斯状态空间模型。更确切地说，我们假设观测方程和状态方程由不一定相等的copula族定义。对于每个时间点，所得到的模型可以描述为C-vine copula，在第一棵树之后截断，其中根节点由潜在状态表示。推理在贝叶斯框架内进行，使用Hamiltonian Monte Carlo方法，其中进一步使用D-vine copula（在第一棵树之后截断）作为先验分布以捕获潜在状态中的时间依赖性。仿真研究表明，基于copula的方法非常灵活，因为它能够描述广泛的依赖结构，同时允许处理缺失数据。应用于大气污染物测量数据表明，我们的方法适合于在存在缺失值的情况下准确建模和预测数据动态。与高斯线性状态空间模型和贝叶斯自适应回归树的比较显示了所提出模型在预测准确性方面的优越性能。