Huijsdens Hester, Leeftink David, Geerligs Linda, Hinne Max
Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen, Thomas van Aquinostraat 4, 6525 GD Nijmegen, The Netherlands.
Entropy (Basel). 2024 Aug 16;26(8):695. doi: 10.3390/e26080695.
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 further 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 in covariance.
计量经济学、神经科学和计算心理学等多个学科研究变量随时间的动态相互作用。一种被称为威沙特过程的贝叶斯非参数模型已被证明在这种情况下是有效的，但其推断仍然极具挑战性。在这项工作中，我们为威沙特过程引入了一种顺序蒙特卡罗（SMC）采样器，并展示了它与传统推断方法（即马尔可夫链蒙特卡罗（MCMC）和变分推断）的比较情况。通过模拟，我们表明SMC采样在动态协方差的估计和样本外预测方面产生了最稳健的结果。当使用具有相关参数的复合协方差函数时，SMC尤其优于其他方法。我们进一步在一个临床抑郁症数据集（n = 1）上证明了我们提出的方法的实际适用性，并展示了如何使用后验分布的准确表示来检验协方差中的动态变化。
