Uncovering Sets of Maximum Dissimilarity on Random Process Data

Published: 28 May 2024, Last Modified: 28 May 2024Accepted by TMLREveryoneRevisionsBibTeX
Abstract: The comparison of local characteristics of two random processes can shed light on periods of time or space at which the processes differ the most. This paper proposes a method that learns about regions with a certain volume, where the marginal attributes of two processes are less similar. The proposed methods are devised in full generality for the setting where the data of interest are themselves stochastic processes, and thus the proposed method can be used for pointing out the regions of maximum dissimilarity with a certain volume, in the contexts of point processes, functional data, and time series. The parameter functions underlying both stochastic processes of interest are modeled via a basis representation, and Bayesian inference is conducted via an integrated nested Laplace approximation. The numerical studies validate the proposed methods, and we showcase their application with case studies on criminology, finance, and medicine.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: Fixed issue with URL. We hope this is okay now. Apologies for the oversight.
Assigned Action Editor: ~Trevor_Campbell1
Submission Number: 2348