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Probability in Statistics

Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
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Setting Limits on Supersymmetry Using Simplified Models
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Published on: November 15, 2013

Probabilities for large events in driven threshold systems.

John B Rundle1, James R Holliday, William R Graves

  • 1Department of Physics, University of California, Davis, California 95616, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

Predicting extreme events like "Black Swans" is crucial. This study introduces a data-driven method using event indexing and information theory to calculate probabilities for large-scale events, like major California earthquakes.

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Area of Science:

  • Complex systems
  • Statistical physics
  • Geophysics

Background:

  • Driven threshold systems often exhibit power-law scaling in event sizes.
  • Predicting the probability of extreme, large-magnitude events ("Black Swans") is a significant challenge.

Purpose of the Study:

  • To develop a data-driven methodology for computing probabilities of extreme events.
  • To apply this method to seismic activity, specifically earthquakes in California.

Main Methods:

  • Transformation to an event index frame.
  • Application of Shannon information theory.
  • Analysis of earthquake event sizes and temporal occurrences.

Main Results:

  • The developed method provides a new approach to assessing extreme event probabilities.
  • For California, the 12-month probability of magnitude >6 earthquakes increases from ~30% post-event to 40%-50% before the next event.

Conclusions:

  • The data-driven event index approach is effective for estimating extreme event probabilities in driven threshold systems.
  • This framework offers valuable insights for seismic hazard assessment and risk management.