Uncovering Regions of Maximum Dissimilarity on Random Process Data

TL;DR

This paper introduces a Bayesian method to identify regions where two stochastic processes differ most significantly, applicable to functional data, time series, and point processes, with validation through numerical studies and real-world case studies.

Contribution

It presents a novel, general Bayesian approach for detecting maximum dissimilarity regions between stochastic processes, extending analysis capabilities across various data types.

Findings

Method effectively identifies dissimilar regions in simulated data.

Application to real-world case studies demonstrates practical utility.

Numerical validation confirms accuracy and robustness.

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 functional data, time series, and point processes. 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.