GU logo Advanced Data Analysis
for the
Physical Sciences
 SUPA logo

University of Glasgow
January 6th - 7th 2009
Overview
This 2-day course, organised by the SUPA Graduate School, and hosted by the Department 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 Department of Physics and Astronomy,   in the Kelvin Building at the University of Glasgow.   (Click  here  for directions to the Department of Physics and Astronomy).    Follow the signs to Room 222 from the main entrance to the Kelvin Building.

On Tuesday 6th January 2009, 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 Dept of Physics and Astronomy



Provisional Schedule and Syllabus (including downloads)
Tuesday 6th Jan
 Room 222, Kelvin Building
10.00 - 11.15     
Introduction and Theoretical Foundations
 Preamble:      ppt file                  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:      ppt file                  pdf file                mp3 file
11.45 - 13.00     
Parameter Estimation: Advanced Line and Curve Fitting
 Section 2:     ppt file                  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:     ppt file                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
    20.00 for 20.30     
Dinner (curry at Mother India)



Wednesday 7th Jan
 Room 222, Kelvin Building
09.30 - 12.45  
An Advanced Toolbox for Bayesian Inference
 Section 4:     ppt file               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:     ppt file               pdf file                 mp3 file
12.45 - 14.00   
Lunch
14.00 - 15.30   
Advanced Numerical Methods
 Section 6:     ppt file             pdf file                  mp3 file

Monte Carlo Methods
  • Generating random numbers: Monte Carlo sampling
  • Inverse problems, smoothing and regularisation
  • Searching large parameter spaces: MCMC methods, inlcuding nested sampling as a tool for efficient Bayesian model selection.
Fourier Methods  (time permitting)
  • Discrete Fourier Transforms and the FFT
  • The Nyquist-Shannon sampling theorem, aliasing and signal reconstruction
 Section 7:     ppt file             pdf file
16.00 - 17.00   
Wrap-up session: group discussion and future plans
 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.
Sivia

 Gregory

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 Tuesday 6th January.   All registered participants will receive an email checking their accommodation requirements.

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