# Bayesian Statistics for Astrophysics (BASTA)

Course
2024-2025

For the Astronomy Bachelor, a passing grade for the course Statistics and Data Analysis (SDA) is required. For the Physics Bachelor, you are very welcome to join this course, but you will need to read up on the material covered in SDA. In addition, a passing grade for Complex Physics of Cooking and Experimentele Natuurkunde is recommended.

## Description

In the era of data science, the responsible and accurate use of statistics is of high importance. In this course we first briefly review the foundations of probability theory and statistics. The main focus is on the application of statistics, in particular parameter inference within the Bayesian framework.
The course covers the following themes:

• Conditional probability and marginalization

• Statistical models and distributions

• Likelihood and its connection to generative models

• Nested models; hypothesis comparison

• Bootstrap confidence intervals

• Bayes' Theorem

• Bayesian inference, including priors

• Markov Chain Monte Carlo methods

• Frequentist versus Bayesian framework comparison

## Course objectives

This course will give an overview of the basic concepts of statistics and probability theory and provide some practical tools for (parameter) inference with typical datasets in physics and astronomy. After this course, you will be able to:

• Explain the difference between least-squares and Bayesian (MCMC) methods for parameter inference

• You can implement these two methods and select the best approach for your dataset

• Examine the outcome of your analysis and critique its assumptions if needed.

In this course, you will be trained in the following skills:

• Problem solving (recognizing and analyzing problems, solution-oriented thinking)

• Analytical skills (analytical thinking, abstraction, evidence)

• Structured thinking (structure, modulated thinking, computational thinking, programming)

• Critical thinking (asking questions, check assumptions)

• Writing instructional Notebooks for your peers

• Team work, collaborative writing

• Using version control software (github)

## Timetable

Schedule

In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.

Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.

Note: Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.

## Mode of instruction

• Lectures (interactive)

• Exercise classes

## Assessment method

There will be a short exam and a written assignment. For the written assignment you will be asked to create one chapter for a website that will contain the lecture notes of this course. You will work in a Python Notebook environment to combine short explanations with code examples. The lecture notes will be combine into a website, to be used by future students of this course (here is one example). You can work in small groups for this written assignment. Each group will also present the content of their chapter in class.

• Written assignment, plus short presentation (50%)

• Written exam (50%)

• No book; relevant material will be distributed via Brightspace

## Registration

As a student, you are responsible for enrolling on time through MyStudyMap.

In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.
Extensive information about the operation of MyStudyMap can be found here.

There are two enrolment periods per year:

• Enrolment for the fall opens in July

• Enrolment for the spring opens in December

Note:

• It is mandatory to enrol for all activities of a course that you are going to follow.

• Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.

• Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.

## Contact

Contact details teacher: Dr. S. van Velzen

## Remarks

Software
Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.