The aim of the present study is to detect abrupt trend changes in the mean of a multidimensional sequential signal. Directly inspired by papers of Fernhead and Liu ([4] and [5]), this work describes the signal in a hierarchical manner : the change dates of a time segmentation process trigger the renewal of a piece-wise constant emission law. Bayesian posterior information on the change dates and emission parameters is obtained. These estimations can be revised online, i.e. as new data arrive. This paper proposes explicit formulations corresponding to various emission laws, as well as a generalization to the case where only partially observed data are available. Practical applications include the returns of partially observed multi-asset investment strategies, when only scant prior knowledge of the movers of the returns is at hand, limited to some statistical assumptions. This situation is different from the study of trend changes in the returns of individual assets, where fundamental exogenous information (news, earnings announcements, controversies, etc.) can be used.

中文翻译：

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多变点和风险评估的在线贝叶斯推理

本研究的目的是检测多维序列信号平均值的突然趋势变化。直接受 Fernhead 和 Liu 论文（[4] 和 [5]）的启发，这项工作以分层方式描述了信号：时间分段过程的变化日期触发了分段恒定发射定律的更新。获得关于变化日期和发射参数的贝叶斯后验信息。这些估计可以在线修改，即随着新数据的到来。本文提出了对应于各种排放规律的明确公式，以及对只有部分观测数据可用的情况的概括。实际应用包括部分观察的多资产投资策略的回报，当手头只有很少的回报推动者的先验知识时，限于一些统计假设。这种情况不同于研究单个资产收益的趋势变化，可以利用基本外生信息（新闻、财报、争议等）。