This course aims to provide an introduction to practical statistics for Astronomers and Physicists, who may have had little (or zero) formal statistics education in their academic careers to date. The course is designed to develop a complex understanding of statistical methods that are applicable to modern scientific inquiry, while drawing examples from astronomy, physics, and outside sources for discussion.
A rough guide to the course modules are outlined below. Throughout the course we will discuss standard statistical biases and mistakes, how these errors influence conclusions and estimated models, and what students can do to fortify their science to common statistical errors. The course will be run in weekly lectures (1.5 hours in duration) and without dedicated exercise classes. The course will have oral examinations. In addition to lecture notes, the course will include many practical examples that will be completed and discussed during the lectures. These will include computational examples covering all aspects of the course, written variously in both R and python.
The lecture time is scheduled to be held weekly on Fridays between 1200-1400. The lecture will be held in GAFO 03/252.
Course Materials
All course materials (lecture notes, slides) are available through the website of the lecturer: here.Course Outline
Data modelling (or "How to describe data")
When working in empirical science, modelling and understanding datasets is paramount. In this module we start by discussing the fundamentals of data modelling. We start by discussing theories of point and interval estimation, in the context of summary statics (e.g. expectation values, confidence intervals), and estimation of data correlation and covariance. Students will learn the fundamentals of data mining and analysis, in a way that is applicable to all physical sciences.
Introduction to Probability (or "How to model data")
For all aspects of modern science, an understanding of probability is required. We cover a range of topics in probability, from decision theory and the fundamentals of probability theory, to standard probabilistic distributions and their origin. From this module, students will gain an insight into different statistical distributions that govern modern observational sciences, the interpretation of these distributions, and how one accurately models distributions of data in an unbiased manner.
Bayesian Statistics
Bayes theorem led to a revolution in statistics, via the concepts of prior and posterior evidence. In modern astronomy and physics, applications of Bayesian statistics are widespread. We begin with a study of Bayes theorem, and the fundamental differences between frequentest and Bayesian analysis. We explore applications of Bayesian statistics, through well studied statistical problems (both within and outside of physics).
Parameter Simulation, Optimisation, & Inference (or "Applying statistics in modern scientific analyses")
We apply our understanding of Bayesian statistics to the common problems of parameter simulation, optimisation, and inference. Students will learn the fundamentals of Monte Carlo Simula- tion, Markov Chain Monte Carlo (MCMC) analysis, hypothesis testing, and quantifying goodness-of-fit. We discuss common errors in parameter inference, including standard physical and astrophysical biases that corrupt statistical analyses.
- Kursleiter/in: Angus Hooper Wright