A pervasive challenge in neuroscience is testing whether neuronal connectivity changes over time due to specific causes, such as stimuli, events, or clinical interventions. Recent hardware innovations and falling data storage costs enable longer, more naturalistic neuronal recordings. The implicit opportunity for understanding the self-organised brain calls for new analysis methods that link temporal scales: from the order of milliseconds over which neuronal dynamics evolve, to the order of minutes, days or even years over which experimental observations unfold. This review article demonstrates how hierarchical generative models and Bayesian inference help to characterise neuronal activity across different time scales. Crucially, these methods go beyond describing statistical associations among observations and enable inference about underlying mechanisms. We offer an overview of fundamental concepts in state-space modeling and suggest a taxonomy for these methods. Additionally, we introduce key mathematical principles that underscore a separation of temporal scales, such as the slaving principle, and review Bayesian methods that are being used to test hypotheses about the brain with multi-scale data. We hope that this review will serve as a useful primer for experimental and computational neuroscientists on the state of the art and current directions of travel in the complex systems modelling literature.

翻译：神经科学面临的一个普遍挑战是检测神经元连接是否因特定原因（如刺激、事件或临床干预）随时间变化。近年来的硬件创新和数据存储成本下降使得更长时间、更接近自然状态的神经元记录成为可能。理解自组织大脑的隐含机遇呼唤着新的分析方法，用于连接从毫秒量级的神经动力学演变到分钟、天甚至年量级的实验观察展开过程的不同时间尺度。本文综述展示了层次化生成模型和贝叶斯推断如何帮助表征不同时间尺度下的神经元活动。关键在于，这些方法不仅限于描述观测数据间的统计关联，还能对潜在机制进行推断。我们概述了状态空间建模的基本概念，并提出了这些方法的分类体系。此外，我们引入了强调时间尺度分离的关键数学原理（如慢变量支配原理），并回顾了利用多尺度数据检验大脑假说的贝叶斯方法。我们希望这篇综述能为实验和计算神经科学家提供关于复杂系统建模文献中前沿进展和当前研究方向的实用入门指南。