Abstract
In an effort to solidly define predictability, and the estimation thereof, in different processes, and considering the interpretation of mutual information as an expected value of the logarithm of joint probability, we show that, in the light of causality, the expected value of the logarithm of conditional probability fulfills the desirable properties of a predictability descriptor. An application to high-resolution rainfall intensity time series is presented.
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Acknowledgements
The authors dedicate this article to the memory of Panagiotis Tsonis, who – in an unpredictable manner – provided the motivation behind this work. Rainfall data were collected at the Hydrometeorology Lab of the Iowa Institute of Hydraulic Research (now IIHR – Hydroscience & Engineering), under the supervision of Konstantine Georgakakos.
Funding
Félix Fernández Méndez acknowledges CONACyT scholarship 485992. Alin A. Carsteanu acknowledges SIP-IPN grant 20230184.
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Fernández Méndez, F., Gómez Larrañaga, J.C. & Carsteanu, A.A. Informational predictability, and an application to the intensity of high-resolution temporal rainfall. Stoch Environ Res Risk Assess 37, 2651–2656 (2023). https://doi.org/10.1007/s00477-023-02410-7
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DOI: https://doi.org/10.1007/s00477-023-02410-7