This is a course which will provide a first introduction to statistical methods in the context of data analysis of physical experiments and astrophysical observations. You will learn how to interpret data and confront it with theoretical models with modern statistical methods. After this course you will be able to independently select from a plethora of statistical tools to modern data analysis.
Statistics - An Introduction
The confrontation of theories with data is at the core of modern sciences. In astrophysics state of the art statistical methods are used to assess and improve models. In this course you will learn from first principles the basics of Bayesian statistics. The course aims that you gain an intuition of which methods to apply in different situations. An important concept is the role of priors. It is only in comparison to prior knowledge that data can inform you about a model. In particular we will study the following topics:
Foundations of Bayesian Statistics
Parameter Estimation - Simple Cases
Parameter Estimation - Advanced Topics
Model Selection
Probabilities
Non-parametric estimation
Design of Experiments
Extensions of Least-Square Methods
Monte Carlo Markov Chain Sampling
The core of the course is not just the lecture. You will learn with hands on problem sheets to tackle statistical problems with the help of experienced tutors.
Please self enroll into the course and register on LSF here and find further information on Moodle.
Literature
The course will mainly follow the book: "Data Analysis: A Bayesian Tutorial" D.S. Sivia (with J. Skilling) Oxford Science Publications (available as e-book from the LMU library)
The statistical distributions are discussed in:
"Statistical Data Analysis" G. Cowan Oxford Science Publications
The MCMC chapter is inspired by:
"Markov Chain Monte Carlo in Practice" W.R. Gilks, S. Richardson and D.J. Spiegelhalter Chapman & Hall/CRC
A nice general introduction to probability: Probability Theory - The Logic of Science E. T. Jaynes Cambridge Univeristy Press (available as e-book from the LMU library)