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The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
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Using Fisher information to track stability in multivariate systems.

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Fisher information (FI) offers a powerful method for analyzing complex systems and identifying trends in data. This study demonstrates FI

Keywords:
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Area of Science:

  • Sustainability Science
  • Data Mining
  • Information Theory

Background:

  • The proliferation of data necessitates advanced techniques for information extraction.
  • Information theory concepts, like Fisher information (FI), are increasingly applied to analyze complex systems.
  • FI quantifies information content and assesses order in system behavior, collapsing variables into a stability index.

Purpose of the Study:

  • To explore the application of Fisher information (FI) in sustainability science and data mining.
  • To demonstrate how FI can analyze patterns, assess system stability, and track trends, including regime shifts.
  • To introduce a novel open-source Python library for computing FI.

Main Methods:

  • Overview of Fisher information (FI) theory.
  • Step-by-step numerical example for computing FI.
  • Application of an open-source Python library to analyze global-mean temperature data (1880-2015).

Main Results:

  • Fisher information (FI) can be effectively applied to sustainability science problems.
  • The developed Python library facilitates the computation and analysis of FI.
  • Analysis of global-mean temperature data revealed significant declines in FI from 1978 onwards.

Conclusions:

  • Fisher information (FI) serves as a valuable tool for assessing system stability and detecting regime shifts in sustainability science.
  • The open-source Python library provides a practical means for researchers to implement FI analysis.
  • The observed decline in FI for global-mean temperature suggests a potential regime shift.