Название: Probability and statistics for geophysical processes
Автор: Demetris Koutsoyiannis
Издательство: National Technical University of Athens
Размер: 1.9 mb
Commonly, probability is regarded to be a branch of applied mathematics that provides tools for data analysis. Nonetheless, probability is a more general concept that helps shape a consistent, realistic and powerful view of the world. Historically, the modern science was initiated from deterministic views of the world, in which probability had a marginal role for peculiar unpredictable phenomena. However, in the turn of the nineteenth century, radical developments in physics, and particularly thermodynamics, dynamical systems and quantum physics, as well as in mathematics has given the probability theory a central role in the scientific scene, in the understanding and the modelling of natural phenomena.
Furthermore, probability has provided grounds for philosophical concepts such as indeterminism and causality, as well as for extending the typical mathematical logic, offering the mathematical foundation of induction. In typical scientific and technological applications, probability provides the tools to quantify uncertainty, rationalize decisions under uncertainty, and make predictions of future events under uncertainty, in lieu of unsuccessful deterministic predictions. Uncertainty seems to be an intrinsic property of nature, as it can emerge even from pure and simple deterministic dynamics, and cannot been eliminated.
This is demonstrated here using a working example with simple deterministic equations and showing that deterministic methods may be good for short-term predictions but for long horizons their predictive capacity is cancelled, whereas the probabilistic methods can perform much better.
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