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Alarm-based prediction:. goals, construction and quality assessment. Ilya Zaliapin Department of Mathematics and Statistics University of Nevada, Reno. Thanks: V. Keilis-Borok, G. Molchan, Y. Kagan, J. Zechar. Global Collaboration and Testing Meeting, April 21, 2008. Prediction goal.
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Alarm-based prediction: goals, construction and quality assessment Ilya Zaliapin Department of Mathematics and Statistics University of Nevada, Reno Thanks: V. Keilis-Borok, G. Molchan, Y. Kagan, J. Zechar Global Collaboration and Testing Meeting, April 21, 2008
Prediction goal Provide information about when and wherean earthquake of specified magnitude will happen. The information does not have to be flawless; possible errors must be evaluated. Prediction at various levels of precision can be practically useful. Often (say, within CSEP framework) we only interested in scientific, independently reproducible prediction methods based on approved data sources.
Prediction quality • Measure of prediction quality is application-specific. It reflects concrete • practical questions that one hope to answer using the prediction results: • - What is the expected long-term damage to a given structure/region? • - What building code to implement? • What insurance rates to set? • What schedule of emergency measures to accept? • What training exercises to perform? • What immediate actions to take in response to prediction? CSEP testing is focused on scientific prediction quality, that is on convenient quality measures, which might be not immediately connected to concrete applications.
Intensity forecasting Alarm-based prediction Prediction outcome Two types of result delivery have been discussed within CSEP: Time Time
Alarm-based prediction: genesis Continuous information (ex: Rundle et al.’s Pattern Informatics method) Time Point information (ex: Shebalin & KB’s RTP, Kossobokov’s M8) Time
Alarm-based prediction: quality assessment Correct alarm False alarm Time Predicted event Failure to predict Quality parameters: n = Proportion of unpredicted EQs t=Total duration of alarms A = Total number of alarms Approach A: Hypothesis testing Quality assessment: Errors of two types Approach B: Contingency analysis Quality assessment: Skill score(s), independence tests
Hypothesis testing approach (Molchan 1990, 1997, 2003, 2008) Problem: Using the information available at time t, decide whether a target EQ will occur within the next D time units. H0: EQ within next D time units H1: No EQ within next D time units Time t Proportion of unpredicted EQs nand alarm duration t are the errors of two types in the hypothesis testing framework.
Hypothesis testing approach (Molchan 1990, 1997, 2003, 2008) Takes into account time dependence (does not assume independent series of trials, as contingency table approach) Specifies the optimal prediction strategy for a broad class of cost functions (tells how to construct prediction) The global optimal strategy coincides with the local optimal strategy, if the cost function is independent of the number of false alarms (each decision is made independently of previous decisions) Optimal strategy is reduced to level crossing by conditional intensity function (justification for level crossing methods)
Optimist strategy: No alarms, All events are missed 1-n-t Pessimist strategy: Always an alarm, All events are predicted Best strategy Error diagram (Molchan, 1990, 1997, 2003, 2008) Failures to predict, n Random guess Alarm duration,t Ideal prediction
Summary Alarm-based prediction is a special form of probabilistic prediction delivery (not a deterministic prediction!) Alarm-based prediction is focused on decision making Error diagram approach provides a convenient paradigm for - constructing optimal predictions - assessing prediction quality Error diagram approach is developed for both time and space-time predictions and is very useful for multi-region prediction experiments Error diagram can complement the likelihood approach in assessing prediction/forecast quality
