Update README.md

Author: VittorioMinio93

README.md

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 FEEDS (Framework for Evaluation of Early Detection Systems) has been developed for the assessment of the generalization capability of a generic Early Detection (ED) system (e.g., Ripepe et al., 2020), which refers to the ability to provide reliable alarms for target events using data different from those used to develop the system. The framework consists of a Python package comprising functions and classes dedicated to the management of geophysical data, simulation in pseudo real-time (i.e., real-time simulation on previously acquired data), and the evaluation of the performance of an alert model. 
 FEEDS assesses the generalization capability of an alert system, i.e., the ability to provide reliable alerts for target events using data different from those with which the system was developed. This evaluation can be quantified through several statistics on predictive parameters (e.g., Cannavò et al., 2017):
 
--TPR (True Positive Rate): represents the ratio between the number of true positives and the total number of eruptive events considered. In other words, it indicates the system's ability to correctly identify positive events. It varies from 0 to 1, respectively in the worst and best cases.
--FDR (False Discovery Rate): this parameter expresses the ratio between the number of false positives and the total number of alerts issued by the system. It helps to assess how much the system generates erroneously positive alarms. It varies from 0 to 1, respectively in the best and worst cases.
--LT (Lead Time): refers to the period of time elapsed between the issuance of the alert and the occurrence of the event. The greater this time, the better the alert system.
--FTA (Fraction Time Alert): indicates the fraction of total time during which the system is in an alert state. A high FTA could indicate an excessive sensitivity of the system, with a period of alarm persistence that would degrade the system's reliability (paradoxically, an FTA of 1, i.e., a system always on alert, would identify all target events with only one alert). The lower this fraction, the better the alert system.
+- TPR (True Positive Rate): represents the ratio between the number of true positives and the total number of eruptive events considered. In other words, it indicates the system's ability to correctly identify positive events. It varies from 0 to 1, respectively in the worst and best cases.
+- FDR (False Discovery Rate): this parameter expresses the ratio between the number of false positives and the total number of alerts issued by the system. It helps to assess how much the system generates erroneously positive alarms. It varies from 0 to 1, respectively in the best and worst cases.
+- LT (Lead Time): refers to the period of time elapsed between the issuance of the alert and the occurrence of the event. The greater this time, the better the alert system.
+- FTA (Fraction Time Alert): indicates the fraction of total time during which the system is in an alert state. A high FTA could indicate an excessive sensitivity of the system, with a period of alarm persistence that would degrade the system's reliability (paradoxically, an FTA of 1, i.e., a system always on alert, would identify all target events with only one alert). The lower this fraction, the better the alert system.
 
 These parameters provide a detailed assessment of the system's performance, allowing for a better understanding of its effectiveness and reliability in detecting specific events such as paroxysms. The distinctive aspect of FEEDS is the application of Monte Carlo cross-validation to an alert system, representing a significant innovation in the field of volcanic prediction.
 The evaluation process of an ED system is complex and involves several phases. These include:
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 You can send an email to vittorio.minio@ingv.it to report suggestions, comments and bugs.
 
 # References
+- Cannavò et al., 2017. A multivariate probabilistic graphical model for real-time volcano monitoring on Mount Etna, Journal of Geophysical Research: Solid Earth.  https://doi.org/10.1002/2016JB013512.
+- Picard and Cook, 1984. Cross-validation of regression models, Journal of the American Statistical Association. https://doi.org/10.2307/2288403.
+- Ripepe et al., 2020. Ground deformation reveals the scale-invariant conduit dynamics driving explosive basaltic eruptions, Nature Communications. https://doi.org/10.1038/s41467-021-21722-2.