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IMA Tutorial

Earthquake Probability Models and Forecasting

Earthquake Probability Models and Forecasting

May 13, 2002, Lind 409

**David
Vere-Jones**

School of Mathematical and Computing Sciences

Victoria University

These two lectures, requiring no advanced prerequisites, will introduce the fascinating subject of mathematical science methods for earthquake forecasting.

**Lecture
1:** *Modeling and Simulation Issues*
(10:00AM - 11:00AM)

What are probability forecasts and why do we need models to provide them? How are appropriate models defined and developed? To illustrate a range of ideas without assuming much technical background, I shall explain how a sequence of models can be defined by simulation algorithms, starting from a simple Poisson process and proceeding to more complex space-, time- and history-dependent models. Such algorithms can also be used as a starting point for forecasting procedures. An important distinction arises in practice between situations where the models cover all aspects of the data required to make the forecast, and situations where the forecasts depend on external variables which lie outside the scope of the models.

**Lecture
2:** *The Assessment and Use of Probability
Forecasts* (11:15AM-12:15PM)

The assessment of probability forecasts hinges on defining a suitable score for the forecasts. Most often the forecasts are dichotomized into "successes" and "failures", but this involves throwing away some of the information in the forecasts. An alternative is to use an "entropy score": if outcome is observed and has forecast probability , we give it the score , or if we want to compare to another (e.g. background) probability . This latter score is just the logarithm of the "probability gain" for the observed outcome.

Usage issues are becoming increasingly important as earthquake forecasts start to become a real posibility. For example, the probability forecasts on Californian earthquakes made by the USGS already have a major and sometimes unintended impact on planning decisions. Are probability forecasts really going to be useful, and, if so, to whom, and how should they be promulgated? Such educational, economic and political issues look just as difficult to tackle as the underlying scientific questions of how and where earthquakes occur.

Mathematics in Geosciences, September 2001 - June 2002