Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data

Abstract

Our ultimate goal is to analyze highly generic data arising from applications as diverse as imaging, biological sciences, atmospheric sciences, or finance, to name a few specific examples. In all these application areas, there is a fundamental reliance on extracting meaningful trends and information from large data sets. Primarily, this is motivated by the fact that in many of these systems, the degree of complexity, or the governing equations, is unknown or impossible to extract. Thus one must rely on data, its statistical properties, and its analysis in the context of spectral methods and linear algebra. 11.1 Basic probability concepts To understand the methods required for data analysis, a review of probability theory and statistical concepts is necessary. Many of the ideas presented in this section are intuitively understood by most students in the mathematical, biolog-ical, physical and engineering sciences. Regardless, a review will serve to refresh one with the concepts and will further help understand their implementation in MATLAB.