Traditional methods for inference in change point detection often rely on a large number of observed data points and can be inaccurate in non-asymptotic settings. With the rise of mobile health and digital phenotyping studies, where patients are monitored through the use of smartphones or other digital devices, change point detection is needed in non-asymptotic settings where it may be important to identify behavioral changes that occur just days before an adverse event such as relapse or suicide. Furthermore, analytical and computationally efficient means of inference are necessary for the monitoring and online analysis of large-scale digital phenotyping cohorts. We extend the result for asymptotic tail probabilities of the likelihood ratio test to the multivariate change point detection setting, and demonstrate through simulation its inaccuracy when the number of observed data points is not large. We propose a non-asymptotic approach for inference on the likelihood ratio test, and compare the efficiency of this estimated p-value to the popular empirical p-value obtained through simulation of the null distribution. The accuracy and power of this approach relative to competing methods is demonstrated through simulation and through the detection of a change point in the behavior of a patient with schizophrenia in the week prior to relapse.

翻译：传统变点检测推断方法通常依赖大量观测数据点，在非渐近设置中可能不准确。随着移动健康与数字表型研究的兴起——患者通过智能手机或其他数字设备被监测——变点检测在非渐近场景中变得必要，例如在复发或自杀等不良事件发生前数日识别行为变化的关键时刻。此外，针对大规模数字表型队列的监测与在线分析，需要兼具分析性与计算高效的推断手段。我们将似然比检验渐近尾部概率的结果扩展至多元变点检测场景，并通过模拟证明当观测数据点数量不足时该方法的非精确性。我们提出一种基于非渐近方法的似然比检验推断框架，并将该估计p值的效率与通过零分布模拟获得的常用经验p值进行比较。通过模拟实验以及对精神分裂症患者复发前一周内行为变点的检测，验证了该方法相较于竞争方法的准确性与统计效能。