Statistical Data Analysis for Practitioners

In science, as well as in our daily lives, we are constantly confronted and dealing with uncertainties. Probability theory and statistics provide the tools to learn from uncertain information and data and to make choices and decisions in the presence of uncertainties.

Goals of the Course

The goals of the lecture are to equip the students with the necessary statistical tools to extract information from noisy data reliably and with quantified uncertainties. The students should be able to identify the common pitfalls of statistical data analysis in their own work and be able to critically assess the quality of published data and statistical analyses. 

Format

Currently, the course is held as a single block on seven consecutive work days. Lectures will be mixed with practical exercises. In these exercises you will mainly apply the widely used Python programming language to perform statistical data analysis yourself.

Practical Course

The practical exercises are designed such that you need only limited programming skills. The exercises consist of Python code, which you have to modify to obtain the desired results. That is, you will choose, set, and modify parameters and select appropriate functions to analyze data. This approach mimics the ubiquitous real-world task to modify someone else’s code for your own purposes.

For the practical course, you need to bring your own laptop. The course material will be made available via Binder online, such that you only need an internet connection. Alternatively, you can use your own Python installation.

For beginners, we offer a short crash course in Python. Programming experience in any language is helpful and recommended but it is not a precondition. You can do the exercises by yourself or pair up with a partner, perhaps with more programming experience.

Lecturers

The lectures and practical course are held alternatingly by three different lecturers according to their core expertise. All lecturers have extensive research experience in statistics and data analysis and teaching experience.

Dr. Jakob Tómas Bullerjahn is a physicist by training and currently working as a postdoctoral research scientist at the Max Plank Institute of Biophysics. His research is devoted to the theoretical description of anomalous and ordinary diffusion processes, in and out of equilibrium. Methodically, Jakob relies on stochastic dynamics and partial differential equations to model his systems of interest, and regularly makes use of likelihoods and statistical tests to analyze experimental and simulation data. He has teaching this lecture on statistics and data analysis since 2021.

Dr. Roberto Covino is an independent group leader at the Frankfurt Institute for Advanced Studies (FIAS). His background is in theoretical and computational physics. His research aims at developing and applying theoretical models, computer simulations, and artificial intelligence methods to understand the emergence of complex biomolecular structures, dynamics, and functions from physical principles. He has been teaching multiple different courses at Goethe University, including a course on biomolecular simulations, membrane biology, and lectures on statistics, data analysis and machine learning.

PD Dr. Jürgen Köfinger is a project leader at Max Planck Institute of Biophysics and has obtained his Habilitation at the Department of Physics of the Goethe University in 2021. He is a physicist by training. Jürgen’s research interests focus on integrative modeling in general and ensemble and force field refinement in particular. In his research, he routinely applies probability and information theory, Bayesian inference, and maximum entropy methods. He has been teaching multiple different courses at Goethe University since 2015 and has been giving this lecture on statistics and data analysis yearly since 2017.

Content

• Basics of probability theory and statistics
  - Elements of probability theory
  - Central limit theorem and standard error of the mean
  - Confidence intervals and p-values
  - Maximum likelihood estimation
  - Bayesian inference

• Statistical inference

  - Model fitting
  - Model comparison

• Time series analysis

  - Autocorrelations
  - Block averaging
  - Bootstrapping / Jackknifing

• Markov chain Monte Carlo o Master equation

  - Monte Carlo sampling
  - Uncertainty quantification

• Machine learning and neural networks

  - Supervised and unsupervised machine learning
  - Clustering
  - Dimensionality reduction
  - Neural networks for regression and classification problems