86840 - PRACTICAL STATISTICS FOR PHYSICS AND ASTROPHYSICS

Learning outcomes

Nontrivial data analysis problems are frequently encountered in modern astronomy, cosmology and physics. They require an understanding of statistical methods, practical skills with software tools and sometimes some ingenuity that comes with experience. The student will gain a practical knowledge of statistical methods and software as applied to many example problems. Basic probability theory will be covered before learning about Bayesian and frequentest inference problems, Monte Carlo techniques, Fisher matrices, random fields, parameter estimation, non-parametric tests, hypothesis testing, and supervised and unsupervised classification and regression problems. The student will become familiar with current software in Python for analysing data and fitting models while getting an understanding of the theory behind them.

Course contents

Starting with the basic probability theory and the classical probability distributions, the course will move on to the theory and practice of modern statistical methods that are widely used in physics and astronomy today. Analytic methods for curve fitting and frequentist parameter estimation will be covered. Numerical Monte Carlo and bootstrap methods will be covered. Then Bayesian inference methods and numerical methods for solving them will be studied. We will then move on to random fields and estimating correlation functions and power spectra from irregularly sampled data. Then image reconstruction from noisy data, Wiener filtering, maximum entropy and deconvolution methods.Finally, if time permits, we will introduce machine learning class and regression methods.

The laboratory part of the course will start with a general introduction to python if needed and then cover the libraries by numpy, scikit and scikit-learn through example projects. The lab will follow the lecture material with practical examples to workout.

1. Random Variable

2. Classic probability distributions

3. The likelihood function and Fisher matrix

Bayesian statistics vs. Frequentist

5. fitting parameters

6. Non-parametric tests Frequentist

7. Random Fields

8. Image reconstruction and map making

9. Numerical methods for the Bayesian Inference problem

10. Model fitting from a machine learning or data science prospective.

Readings/Bibliography

Lecture notes will be the most important.

Reference texts:

DeGroot and Schervish, Probability and Statistics, Addison Wesley
P. Gregory, Bayesian Logical Data Analysis for Physical Sciences, Cambridge University Press

Teaching methods

The course will consist of a combination of lectures to introduce theory and a computer lab where practical skill will be developed.

Assessment methods

Oral or written exams.

Teaching tools

Blackboard, video projector, and computer lab.

Links to further information

https://rbmetcalf.github.io/Practical-Statistics/

Office hours

See the website of Robert Benton Metcalf