We propose a flexible nonparametric Bayesian modelling framework for multivariate time series of count data based on tensor factorisations. Our models can be viewed as infinite state space Markov chains of known maximal order with non-linear serial dependence through the introduction of appropriate latent variables. Alternatively, our models can be viewed as Bayesian hierarchical models with conditionally independent Poisson distributed observations. Inference about the important lags and their complex interactions is achieved via MCMC. When the observed counts are large, we deal with the resulting computational complexity of Bayesian inference via a two-step inferential strategy based on an initial analysis of a training set of the data. Our methodology is illustrated using simulation experiments and analysis of real-world data.

翻译：我们提出了一种基于张量分解的灵活非参数贝叶斯建模框架，适用于多元计数时间序列数据。通过引入适当的潜变量，我们的模型可视为具有已知最大阶数且存在非线性序列依赖的无限状态空间马尔可夫链。另一种视角是，我们的模型可视为条件独立泊松分布观测下的贝叶斯分层模型。关于重要滞后项及其复杂交互作用的推断通过MCMC实现。当观测计数较大时，我们采用基于初始训练集数据的两步推断策略来处理贝叶斯推断的计算复杂性。通过模拟实验和真实数据分析验证了该方法的有效性。