标题： 关于时变动态贝叶斯推理的教程 显示英文标题

标题： A Tutorial on Time-Evolving Dynamical Bayesian Inference

摘要： 鉴于目前可获得的测量数据的数量和种类日益增加，人们对于能够成功应对分析数据时常出现的相关问题的强大信号处理工具的需求也越来越大。 实际上，许多数据生成系统不仅具有时间变异性，还受到邻近系统的干扰，并且会受到环境中的随机波动（噪声）的影响。 为了涵盖这类问题，我们提供了一个关于在噪声存在下动态贝叶斯推断随时间演化的耦合系统的教程。 该教程包括必要的理论描述以及其实现算法。 为了通用编程的目的，还给出了伪代码描述。 基于耦合相位振荡器和极限环振荡器的例子展示了相位动力学推断的关键特征。 状态域推断通过耦合混沌振荡器的例子来说明。 后者的应用范围被概述为基于耦合函数调制的安全通信。 Matlab代码用于实现该方法以及具体示例，随附于本教程中。 显示英文摘要

摘要： In view of the current availability and variety of measured data, there is an increasing demand for powerful signal processing tools that can cope successfully with the associated problems that often arise when data are being analysed. In practice many of the data-generating systems are not only time-variable, but also influenced by neighbouring systems and subject to random fluctuations (noise) from their environments. To encompass problems of this kind, we present a tutorial about the dynamical Bayesian inference of time-evolving coupled systems in the presence of noise. It includes the necessary theoretical description and the algorithms for its implementation. For general programming purposes, a pseudocode description is also given. Examples based on coupled phase and limit-cycle oscillators illustrate the salient features of phase dynamics inference. State domain inference is illustrated with an example of coupled chaotic oscillators. The applicability of the latter example to secure communications based on the modulation of coupling functions is outlined. MatLab codes for implementation of the method, as well as for the explicit examples, accompany the tutorial.