Sequential testing and change detection algorythms

我建议在顺序统计算法和变化点分析领域进行研究。当观察结果在一段时间内一个接一个地出现时，顺序测试是必要的。正在进行监测，以发现数据生成机制的变化，例如气候变化、制造质量等。在我早期的工作中，已经为独立观测情况定义了新型算法。这些方法优于现有的方法，因为尽管在发生变化后的反应时间最小化是最佳的，但它们具有不可接受的I型误差。这就是为什么许多顺序测试方法主要停留在理论领域，而实践者没有广泛地采用它们的原因。新算法对第一类错误有严格的控制，易于执行，并且在发出警报（声明数据生成机制已经更改）时只稍微增加了延迟时间。在解决了独立观测的这一问题后，必须考虑其他数据结构，因为独立性假设在实践中经常被违反。对于实践中出现的不同时间序列观测，工作正在进行和扩大。在临床试验中出现的数据结构是特别有趣的。对它们进行序贯监控的实现是建立在解决理论上具有挑战性的问题的基础上的。变化点检测：在这些算法中，我们回顾数据，看看是否有任何干扰发生。这些方法是必不可少的，因为如果在数据生成过程中存在结构变化，并且没有检测到，那么所有的模型拟合和预测都是错误的。这些方法的潜在和现有应用是环境数据分析、计量经济学、生物统计学等。

I propose to do research in the areas of Sequential Statistical Algorithms and Change-Point Analysis.1. Sequential Testing is necessary when observations come in one by one over a period of time. Monitoring is ongoing to detect change in the data generating mechanism, such as change in climate, manufacturing quality, etc. In my earlier work new type of algorithms have been defined for the independent observations case. These are superior to existing methods as, although optimal for minimizing the reaction time after change had occurred, those have unacceptable type I error. This is the reason why many sequential testing methods remained mostly in the theoretical domain, and practitioners have not adapted them widely. The new algorithms have tight control over type I errors, easy to perform, and pay for this with only slightly increased delay time in raising alarm (declaring that the data generating mechanism has changed). Having solved this problem for independent observations other data structures have to be considered as the independence assumptions are often violated in practice. Work is ongoing and expanding for different time series observations that are arising in practice.  Data structures that arise in clinical trials are of special interest. The implementation of sequential monitoring for them is based on solving theoretically challenging problems.2. Change-Point Detection: In these algorithms we look at the data retrospectively to see if any disturbance has occurred. Such methods are essential, as if there was a structural change in the data generating procedure, and it was not detected, then all model fitting and forecast are erroneous. Potential and existing applications of these methods are in environmental data analysis, econometrics, biostatistics, etc.