title: Using Fisher information to track stability in multivariate systems.
abstract: With the current proliferation of data, the proficient use of statistical and mining techniques offer substantial benefits to capture useful information from any dataset. As numerous approaches make use of information theory concepts, here, we discuss how Fisher information (FI) can be applied to sustainability science problems and used in data mining applications by analysing patterns in data. FI was developed as a measure of information content in data, and it has been adapted to assess order in complex system behaviour. The main advantage of the approach is the ability to collapse multiple variables into an index that can be used to assess stability and track overall trends in a system, including its regimes and regime shifts. Here, we provide a brief overview of FI theory, followed by a simple step-by-step numerical example on how to compute FI. Furthermore, we introduce an open source Python library that can be freely downloaded from GitHub and we use it in a simple case study to evaluate the evolution of FI for the global-mean temperature from 1880 to 2015. Results indicate significant declines in FI starting in 1978, suggesting a possible regime shift.
authors.affiliation: Complex and Sustainable Urban Networks (CSUN) Laboratory , University of Illinois at Chicago , Chicago, IL , USA.
authors.forename: Nasir
authors.identifier: 0000-0001-5067-7368
authors.initials: N
authors.lastname: Ahmad
authors.affiliation: Complex and Sustainable Urban Networks (CSUN) Laboratory , University of Illinois at Chicago , Chicago, IL , USA.
authors.forename: Sybil
authors.initials: S
authors.lastname: Derrible
authors.affiliation: Sustainable Technology Division, Office of Research and Development , US Environmental Protection Agency , Cincinnati, OH , USA.
authors.forename: Tarsha
authors.initials: T
authors.lastname: Eason
authors.affiliation: Sustainable Technology Division, Office of Research and Development, US Environmental Protection Agency, Cincinnati, OH, USA; Faculty of Information Technology and Bionics, Pazmany Peter Catholic University, Budapest, Hungary.
authors.forename: Heriberto
authors.initials: H
authors.lastname: Cabezas
keywords: Fisher information; big data; data mining; information science