SUPA Data analysis course

Advanced Data Analysis
for the
Physical Sciences

University of Glasgow
January 5th - 6th 2011

Overview

This 2-day course, organised by the SUPA Graduate School, and hosted by the School of Physics and Astronomy at the University of Glasgow, will provide a comprehensive introduction to the principles and practice of advanced data analysis, with particular focus on their application within the physical sciences.

During the course, a range of topics will be explored, via a series of lectures and discussions.

SUPA ADA Intended Learning Outcomes: download

Day One: Core Topics

Day Two: Advanced Topics

Theoretical foundations, and the nature of probability
The essentials of line and curve fitting
An introduction to Bayesian inference
Bayesian vs frequentist hypothesis testing, and goodness of fit statistics

Covariance and the Fisher matrix
Bayesian evidence and model selection
Efficient techniques for generating random numbers
Bayesian inference with very large parameter spaces: Markov Chain Monte Carlo methods

Short cut to downloads

Short cut to weblinks

The data analysis course is open to all Scottish postgraduate students in physics and astronomy, but is aimed in particular at first year postgraduates. If you are interested in attending, but are unsure if the course will be appropriate, you should discuss it first with your supervisor or local SUPA Graduate School representative.

There is no registration fee for the data analysis course. For SUPA students who are not from Glasgow University, your travel and / or subsistence costs for attendance will be met by the SUPA Graduate School. Contact your local Graduate School representative to check that you are eligible for funding support.

Practical Information

The data analysis course will be held in Room 222 of the School of Physics and Astronomy, in the Kelvin Building at the University of Glasgow. Follow the signs to Room 222 from the main entrance to the Kelvin Building.

On Wednesday 5th January 2011, the course lectures will begin in Room 222 at 10am.

During the breaks, tea, coffee and soft drinks will be available in Room 470, the Kelvin Building Common Room. Follow the signs to the Common Room from outside Room 222 (or ask one of the local students!).

Kelvin Building, University of Glasgow.
Home to the School of Physics and Astronomy

Provisional Schedule and Syllabus (including downloads)

Wed 5th Jan

Room 222, Kelvin Building

10.00 - 11.15

Introduction and Theoretical Foundations

Preamble: pdf file mp3 file

The meaning of probability: Bayesian and frequentist approaches
Rules for combining probabilities; Bayes' theorem
Discrete and continuous distributions
Uniform, Poisson and normal distributions
Measures and moments of a distribution
Multivariate distributions; joint pdfs; correlation; marginal and conditional distributions

Section 1: pdf file mp3 file

11.45 - 13.00

Parameter Estimation: Advanced Line and Curve Fitting

Section 2: pdf file mp3 file

Least squares; linear and non-linear regression
The principle of maximum likelihood
Connections to elementary treatments of line and curve fitting; practical numerical considerations
Bayes' theorem applied to parameter estimation
Priors, likelihoods and posterior distributions

13.00 - 14.15

Lunch

14.15 - 17.00

Hypothesis Testing and Goodness-of-Fit

Section 3: pdf file mp3 file

Significance of a hypothesis test
Simple hypothesis tests with the normal distribution
Student's t tests
The chi-squared statistic and goodness-of-fit
Testing for statistical independence
Determining confidence regions
Introduction to Bayesian hypothesis testing

from 17.30

Informal gathering in pub

19.00 for 19.30

Dinner (curry at Mother India)

Thu 6th Jan

Room 222, Kelvin Building

09.30 - 12.45

An Advanced Toolbox for Bayesian Inference

Section 4: pdf file mp3 file

Gaussian approximation to the posterior pdf
The Fisher information matrix
Data compression: principal component analysis, SVD and independent component analysis
Assigning prior probabilities: the principle of insufficient reason; maximum entropy
Bayesian model selection: prior odds and the Bayes' Factor; Bayesian Evidence; Occam's razor

Section 5: pdf file mp3 file

12.45 - 14.00

Lunch

14.00 - 15.30

Advanced Numerical Methods

Section 6: pdf file mp3 file

Generating random numbers: Monte Carlo sampling
Inverse problems, smoothing and regularisation
Searching large parameter spaces: MCMC methods and nested sampling.
Discrete Fourier transforms and the FFT.
The Nyquist-Shannon sampling theorem.

SUPAADA problem sheet: download

Course Materials

Copies of the lecture notes and other material will be be available online.

Podcasts of the lectures will also be available after the course.

Much of the course syllabus is well covered in Data Analysis: A Bayesian Tutorial, by D.S. Sivia and J. Skilling, and in Bayesian Logical Data Analysis for the Physical Sciences, by Phil Gregory.

Some of the more advanced material is covered in Information Theory, Inference and Learning Algorithms, by D. Mackay. This book is also available online.

Links to external websites and other resources

Face recognition software (just for fun!)

Supplementary notes on hypothesis testing

Introductory statistics lecture notes

The Prosecutor's fallacy: examples of misunderstanding probability

Online matrix calculator

Numerical Recipes books online

Links to webpages that perform statistical calculations online

Accommodation

For SUPA students from outside Glasgow, the organisers can arrange accommodation in a nearby hotel for the night of Wednesday 5th January. All registered participants will receive an email checking their accommodation requirements.

Martin Hendry (principal organiser and course lecturer)
School of Physics and Astronomy
University of Glasgow