Prior attendance of introductory statistics courses is helpful but not a mandatory prerequisite. Basic programming skills, or the will to develop these, are expected.
Randomness, uncertainties and deviations from the norm surround us in everyday life. A major asset of any scientist is to see beyond the complexity of noise, scatter and biases, and to find an underlying -often surprisingly simple- explanation for the noisy data. This course is specialized to astronomical data analysis, but the topics discussed will also foster an improved understanding of Google, Facebook and other free social media services.
Topics that will be covered include:
Descriptive statistics: Finding meaning in a huge data set.
Inference statistics: Constraining a physical model by data.
Filtering, e.g. for gravitational wave detections and source detection.
Random fields: Sky surveys and structure formation in cosmology.
Sampling methods: Making huge data analyses numerically feasible.
Bayesian Hierarchical Models: How to disentangle a seemingly complex analysis.
Prior Theory and Information Measures: How not to hide prejudices in an analyses.
Missing data and elusive physics: What to do if your sought signal hides in the dark figures?
Machine learning: Finding patterns which escape humans.
Principal course objective: After completion of this course, you will be able to correctly interpret noisy data. You will be able to design and apply statistical methods to answer scientific questions. You will be able to measure parameters, discover astronomical objects, or discover elusive signals in noisy data.
Upon completion of this course, you will be able to:
Recognize the most common distributions of noisy astronomical data
Identify signals in noisy data
Reject theories which are incompatible with data
Design own statistical methods to analyze complex data
Categorize astronomical objects
Solve simple Bayesian Hierarchical Models
Discover prejudices in analyses
Explain basic machine learning algorithms
In this course, you will be trained in the following behaviour-oriented skills:
Problem solving (recognizing and analyzing problems, solution-oriented thinking)
Critical thinking (asking questions, check assumptions)
Analytical skills (analytical thinking, abstraction, evidence)
Creative thinking (resourcefulness, curiosity, thinking out of the box)
Mode of instruction
Lectures on Monday, with bi-weekly numerical tutorial sessions on Thursday. One exercise sheet containing analytical and numerical problems will be handed out on Mondays. These are to be tackled proactively by the students. The Thursday tutorials will cover the analytical solutions, provide programming support, and help interpret the results. The programs thus developed can be used in the exam.
Written exam (analytical part, accounting for 50% of grade), see the Astronomy master examination schedules
Practical exam (numerical part, accounting for 50% of grade)
Upon completion of the analytical part, you can proceed to the numerical part, where you are allowed to use your own programs in order to now analyze a testdata set. An example exam will be uploaded at the beginning of the course.