Statistics and Data Analysis

We introduce the basics of probability theory, classical statistics, and classical error analysis (uncertainty quantification, p-values, confidence intervals), which serve as starting points to explore modern methods of statistics (maximum likelihood, Bayes, machine learning). We use these methods to extract information from noisy data through linear and nonlinear parameter estimation (fitting) and model comparison. We show how to analyze data containing dynamical information by time series analysis (correlation functions, block averaging) and Markov chain Monte Carlo simulations. We introduce and discuss the main concepts of machine learning and discuss supervised and unsupervised learning, including state-of-the art clustering methods and neural networks. In the practical course, students learn to use these tools by adapting functions and scripts written in a modern programming language. They explore fundamental principles of probability theory, statistics, and machine learning. They learn the principles underlying these tools and how to apply them by analyzing data in practical examples taken from diverse areas of biophysics.