We present a simple reduction from sequential estimation to sequential changepoint detection (SCD). In short, suppose we are interested in detecting changepoints in some parameter or functional $\theta$ of the underlying distribution. We demonstrate that if we can construct a confidence sequence (CS) for $\theta$, then we can also successfully perform SCD for $\theta$. This is accomplished by checking if two CSs -- one forwards and the other backwards -- ever fail to intersect. Since the literature on CSs has been rapidly evolving recently, the reduction provided in this paper immediately solves several old and new change detection problems. Further, our "backward CS", constructed by reversing time, is new and potentially of independent interest. We provide strong nonasymptotic guarantees on the frequency of false alarms and detection delay, and demonstrate numerical effectiveness on several problems.

翻译：我们提出了一种从序贯估计到序贯变化检测（SCD）的简单归约方法。简言之，假设我们关注于检测底层分布中某个参数或泛函$\theta$的变化点。我们证明，若能构造出$\theta$的置信序列（CS），则也可成功实现针对$\theta$的序贯变化检测。具体方法是通过检验两条置信序列——一条向前、另一条向后——是否始终存在交集。由于近年来关于置信序列的研究迅速发展，本文提供的归约方法能立即解决多个新老变化检测问题。此外，我们通过反转时间构建的"向后置信序列"是全新的概念，可能具有独立的研究价值。我们为虚警频率和检测延迟提供了强非渐近性保证，并在多个问题上展示了数值有效性。