Abstract

The analysis of solar irradiance has important applications in predicting solar energy production from solar power plants. Although the sun provides every day more energy than we need, the variability caused by environmental conditions affects electricity production. Most of the existing statistical models to forecast solar irradiance are linear and highly depend on normality assumptions. However, solar irradiance shows strong non-linearity and is only measured during the day time. Thus, we propose a new multi-day threshold autoregressive (TAR) model to quantify the variability of the daily irradiance time series. When we apply our model to study the statistical properties of observed irradiance data in the Guadeloupe island group, a French overseas region located in the southern Caribbean Sea, we are able to characterize two states of the irradiance series. These states represent the clear-sky and non-clear-sky regimes. Using our model we are able to simulate irradiance series that behave similar to the real data in mean and variability, and more accurate forecasts compared to its competitors. 

Brief Biography

Dr. Carolina Euan is a postdoctoral fellow at the Environmental Statistics Research Group at King Abdullah University of Science and Technology (KAUST). Carolina Euan received her Ph.D. degree in Probability and Statistics from the Center for Research in Mathematics (CIMAT), Mexico, in 2016.  She joined KAUST as a Postdoctoral Research Fellow in October 2016. Her research interests are the analysis of High dimensional Time Series, Spatio-Temporal Models, Non-Stationary Processes and Complex Data Visualization.

Abstract

The mini-course is an introduction to the analysis of infinity−harmonic functions, a subject that grew mature in recent years in the field of nonlinear partial differential equations. The material covered ranges from the Lipschitz extension problem to questions of existence, uniqueness and regularity for infinity−harmonic functions. A rigorous and detailed analysis of the equivalence between being absolutely minimising Lipschitz, enjoying comparison with cones and solving the infinity–Laplace equation in the viscosity sense is the backbone of the course. A few regularity results (including the Harnack inequality and the local Lipschitz continuity) and an easy proof, due to Armstrong and Smart, of the celebrated uniqueness theorem of Jensen complete the course.

Brief Biography

José Miguel Urbano is a Professor of Mathematics at the University of Coimbra. He holds a PhD from the University of Lisbon and did a postdoc at Northwestern University in Chicago. He is the author of the book The Method of Intrinsic. Scaling and of over 50 scientific papers in the area of Nonlinear Partial Differential Equations. He has supervised four PhD students and ten postdoctoral fellows and is an associate editor of the journal Nonlinear Analysis. He was a member of the Scientific Council for the Exact Sciences and Engineering of the Portuguese Science Foundation (FCT) and has served as evaluator of grants and research projects for the EU (Marie-Curie Fellowships), ERC (Starting Grants), the Academy of Finland, the Latvian Council of Science and FCT. He has taught short courses at IMPA (Rio de Janeiro, Brazil), the University of Florence (Italy), Aalto University (Finland), the Federal University of Ceará (Fortaleza, Brazil), KAUST (Saudi Arabia) and Seoul National University (South Korea). 

Abstract

Functional data analysis is a very active research area due to the overwhelming existence of functional data. In the first part of this talk, I will introduce how functional data depth is used to carry out exploratory data analysis and explain recently-developed depth techniques. In the second part, I will discuss spatio-temporal statistical modeling. It is challenging to build realistic space-time models and assess the validity of the model, especially when datasets are large. I will present a set of visualization tools we developed using functional data analysis techniques for visualizing covariance structures of univariate and multivariate spatio-temporal processes. I will illustrate the performance of the proposed methods in the exploratory data analysis of spatio-temporal data.

Brief Biography

Huang Huang is a research scientist in the Spatio-Temporal Statistics & Data Science group at KAUST. Before working at KAUST, he did research on statistical computing for climate applications as a postdoc at the National Center for Atmospheric Research (NCAR), the Statistical and Applied Mathematical Sciences Institute (SAMSI), and Duke University. His research interest includes spatio-temporal statistics, functional data analysis, Bayesian modeling, machine learning, and high-performance computing for large datasets.

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