GU logo Advanced Data Analysis
for the
Physical Sciences

SUPA logo

University of Glasgow
January 5th - 6th 2011


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:  

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


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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
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   

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   
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


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