Statistical Methods for the Physical Sciences

Course manual 2025/2026

Course content

Data is everywhere! It now plays a vital part in nearly every aspect of human decision making and is just as important in scientific research. This is especially true in physics and astronomy, where our understanding depends heavily on observations of the natural world. But how do we turn raw data into meaningful knowledge about nature? How can we make sense of the claims we encounter in scientific literature, or in the news? This is where statistics comes in. Statistics, grounded in the mathematics of probability and logic, provides the tools we need to extract insights from data. These methods are not only central to academic research but are also fundamental in a wide range of careers, from data science to finance. 

This course offers an intensive introduction to statistical methods and probabilistic thinking, with a focus on interpreting data in astronomy and the physical sciences. While rooted in scientific research, the skills gained have wide-reaching applications beyond it. The course begins by establishing a solid mathematical foundation, providing the tools to adapt statistical methods to new situations. Building on this base, it emphasises intuition and hands-on experience over abstract proofs, focusing on practical skills that can be applied right away. Through intensive training with Python-based data analysis challenges, you’ll learn to work with real data from physics and astronomy and gain a solid understanding of where and how to apply statistical methods.

Study materials

Literature

• Simon Vaughan, 'Scientific Inference: Learning from Data', Cambridge University Press, 2013, ISBN 9781107607590.

Practical training material

• https://huppenkothen.org/stats-methods-26/

Software

• Python + scientific software stack

Objectives

• Explain the foundational concepts of statistics, including probability, randomness, statistical distributions.
• Formulate a statistically robust data analysis process that considers the limitations of the statistical methods used and the data to be analysed.
• Choose an appropriate statistical test for a given problem, and employ hypothesis testing to make inferences about data.
• Apply Bayesian probability theory to scientific problems.
• Develop simple computer programmes to analyse data and apply statistical testing in practice.
• Critically interpret the results of a statistical test, including an evaluation of the appropriateness of the test, and its assumptions and limitations, in comparison to the data.
• Evaluate scientific results in the academic literature within physics/astronomy and in popular media.

Teaching methods

• Lecture
• Computer lab session/practical training
• Self-study

Interactive lectures introduce the relevant maths and background, with exercises. Tutorials include more exercises to prep for exam, and help with the assignments. The assignments and tutorials train students to use statistical thinking and methods in a real-world data analysis context. They are designed to be useful preparation for MSc thesis work, if it uses data, and also trains students in skills and methods useful for careers outside of academia and physics. 

Learning activities

Attendance

Assessment

Exams are in-person and handwritten, a guide with the concepts to be assessed and the formula sheet shared during the exam will be shared on Canvas. Students are should bring writing utensils and a graphical calculator to the exam. Other materials are not allowed. The resit will be similar and difficulty and length to the initial exam.

There is no resit for the assignment. Late work which is submitted up to 24 hours after the deadline will receive a penalty of -20% of the awarded grade, while work submitted 24-48 hours after the deadline will receive a penalty of -40% of the awarded grade. Work submitted later than this will not be assessed. The rubric for the assessment of all the assignments, listing the categories assessed and the requirements for each of them, will be provided separately on Canvas.

Inspection of assessed work

Contact the course coordinator to make an appointment for inspection.

Assignments

There are two assignments for this course, each will involve putting the statistical concepts learned in class into practice through a series of guided data analysis exercises, to be performed in Python on a computer. We expect students to help each other, especially early on and on coding tasks, but assignments must be submitted individually and clearly recognisable as each student's own work. The assignments are graded and each accounts for 25% of the course grade.

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Additional information

Recommended prior knowledge: Physics/astrophysics or similar mathematics-based courses at the Bachelor level. A basic knowledge of Python programming is also important for the practical exercises.

Contact information

Coordinator

• dr. D. Huppenkothen MSc