Functional data often has a hierarchical structure, such as repeat measurements of a single process under varying conditions. Given a hierarchical dataset of function observations one might be concerned with determining if the system generating the function realizations has changed significantly. Gaussian processes (GPs) have been used to model this type of hierarchical data, and have also been used for outlier detection but little work has been done on using hierarchical GPs for outlier detection. To this end we explore the use of GPs on hierarchical functional data for flagging such outlying function realizations.
We illustrate this approach on both real and simulated data with the goal of identifying drift in the generating process. This approach is developed in order to provide a black box which practitioners can use to flag newly generated observations while they are being collected so as to avoid wasting lab resources on faulty measurements. Results are compared with simpler methods in order to determine if the added complexity of GPs is justified by increased performance.
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