On Spatio Temporal Data Modelling And Uncertainty Quantification Using Machine Learning And Information Theory
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On Spatio-Temporal Data Modelling and Uncertainty Quantification Using Machine Learning and Information Theory
The gathering and storage of data indexed in space and time are experiencing unprecedented growth, demanding for advanced and adapted tools to analyse them. This thesis deals with the exploration and modelling of complex high-frequency and non-stationary spatio-temporal data. It proposes an efficient framework in modelling with machine learning algorithms spatio-temporal fields measured on irregular monitoring networks, accounting for high dimensional input space and large data sets. The uncertainty quantification is enabled by specifying this framework with the extreme learning machine, a particular type of artificial neural network for which analytical results, variance estimation and confidence intervals are developed. Particular attention is also paid to a highly versatile exploratory data analysis tool based on information theory, the Fisher-Shannon analysis, which can be used to assess the complexity of distributional properties of temporal, spatial and spatio-temporal data sets. Examples of the proposed methodologies are concentrated on data from environmental sciences, with an emphasis on wind speed modelling in complex mountainous terrain and the resulting renewable energy assessment. The contributions of this thesis can find a large number of applications in several research domains where exploration, understanding, clustering, interpolation and forecasting of complex phenomena are of utmost importance.
On Spatio-Temporal Data Modelling and Uncertainty Quantification Using Machine Learning and Information Theory
The gathering and storage of data indexed in space and time are experiencing unprecedented growth, demanding for advanced and adapted tools to analyse them. This thesis deals with the exploration and modelling of complex high-frequency and non-stationary spatio-temporal data. It proposes an efficient framework in modelling with machine learning algorithms spatio-temporal fields measured on irregular monitoring networks, accounting for high dimensional input space and large data sets. The uncertainty quantification is enabled by specifying this framework with the extreme learning machine, a particular type of artificial neural network for which analytical results, variance estimation and confidence intervals are developed. Particular attention is also paid to a highly versatile exploratory data analysis tool based on information theory, the Fisher-Shannon analysis, which can be used to assess the complexity of distributional properties of temporal, spatial and spatio-temporal data sets. Examples of the proposed methodologies are concentrated on data from environmental sciences, with an emphasis on wind speed modelling in complex mountainous terrain and the resulting renewable energy assessment. The contributions of this thesis can find a large number of applications in several research domains where exploration, understanding, clustering, interpolation and forecasting of complex phenomena are of utmost importance.
Foundations of Probability Theory
"Foundations of Probability Theory" offers a thorough exploration of probability theory's principles, methods, and applications. Designed for students, researchers, and practitioners, this comprehensive guide covers both foundational concepts and advanced topics. We begin with basic probability concepts, including sample spaces, events, probability distributions, and random variables, progressing to advanced topics like conditional probability, Bayes' theorem, and stochastic processes. This approach lays a solid foundation for further exploration. Our book balances theory and application, emphasizing practical applications and real-world examples. We cover topics such as statistical inference, estimation, hypothesis testing, Bayesian inference, Markov chains, Monte Carlo methods, and more. Each topic includes clear explanations, illustrative examples, and exercises to reinforce learning. Whether you're a student building a solid understanding of probability theory, a researcher exploring advanced topics, or a practitioner applying probabilistic methods to solve real-world problems, this book is an invaluable resource. We equip readers with the knowledge and tools necessary to tackle complex problems, make informed decisions, and explore probability theory's rich landscape with confidence.