Several disciplines, such as econometrics, neuroscience, and computational psychology, study the dynamic interactions between variables over time. A Bayesian nonparametric model known as the Wishart process has been shown to be effective in this situation, but its inference remains highly challenging. In this work, we introduce a Sequential Monte Carlo (SMC) sampler for the Wishart process, and show how it compares to conventional inference approaches, namely MCMC and variational inference. Using simulations we show that SMC sampling results in the most robust estimates and out-of-sample predictions of dynamic covariance. SMC especially outperforms the alternative approaches when using composite covariance functions with correlated parameters. We demonstrate the practical applicability of our proposed approach on a dataset of clinical depression (n=1), and show how using an accurate representation of the posterior distribution can be used to test for dynamics on covariance

翻译：在计量经济学、神经科学和计算心理学等多个学科中，研究者常需探究变量间随时间变化的动态交互关系。一种被称为Wishart过程的贝叶斯非参数模型已被证明在此类情境中具有良好效果，但其推断过程仍极具挑战性。本研究针对Wishart过程提出了一种序贯蒙特卡罗（SMC）采样器，并通过与传统的马尔可夫链蒙特卡罗（MCMC）及变分推断方法进行比较，展示了其优势。仿真实验表明，SMC采样法能获得最稳健的动态协方差估计样本外预测结果。当使用参数相关的复合协方差函数时，SMC方法的表现尤为突出，显著优于其他替代方案。我们在临床抑郁症数据集（n=1）上验证了所提方法的实际适用性，并展示了如何利用精确的后验分布表征来检验协方差的动态特性。