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The Monte Carlo method is a numerical technique to model the probability of all possible outcomes in a process that cannot easily be predicted due to the interference of random variables. It is a technique used to understand the impact of uncertainty, ambiguity, and risk in forecasting models. This book is organized into three sections and presents the general principles of the Monte Carlo method with an emphasis on techniques to decrease simulation time and increase accuracy. Section 1 discusses the major fields of application of the Monte Carlo method in medicine. Section 2 introduces the theory and application of the Monte Carlo method in material science. Section 3 provides practical information needed to support simulation and analysis of structures by numerical models and intr... |
The overarching aim of this open access book is to present self-contained theory and algorithms for investigation and prediction of electric demand peaks. A cross-section of popular demand forecasting algorithms from statistics, machine learning and mathematics is presented, followed by extreme value theory techniques with examples. In order to achieve carbon targets, good forecasts of peaks are essential. For instance, shifting demand or charging battery depends on correct demand predictions in time. Majority of forecasting algorithms historically were focused on average load prediction. In order to model the peaks, methods from extreme value theory are applied. This allows us to study extremes without making any assumption on the central parts of demand distribution and to predict... |
