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：传统的变点检测推理方法常常依靠大量观察数据点，这种方法在非渐近式场景下容易出现不准确的问题。随着移动健康和数字表型研究的兴起，需要在非渐近式场景下进行变点检测，以便及时发现与不良事件（如复发或自杀）相关的行为变化，这必须在出现变化的数天内完成。此外，在大规模数字表型队列的监测和在线分析中，需要分析效率高并且具有计算能力的推理方法。将似然比检验的渐近尾部概率结果扩展到多元变点检测设置中，演示了在观察数据点不多时似然比检验不准确的问题。我们提出了一种用于似然比检验推理的非渐近式方法，并将其估计的p值的效率与通过模拟零分布得到的常用经验p值进行比较。通过模拟和在患有精神分裂症的患者中检测出复发前一周的行为变化，证明了该方法相对于竞争方法的准确性和功效。