Advanced methods in statistical data analysis

19 Oct 2009, 09:00 → 23 Oct 2009, 18:00 Europe/Copenhagen

Aud A (Blegdamsvej) mornings - Canteen (Rockefeller) afternoons. Friday Rockecfeller (auditorium + canteen) all day

This elite PhD course in Copenhagen will provide the students with a wide overview of the most advanced statistical methods used for data analysis.

Teachers: Dr. Wouter Verkerke and Prof.Andrew Liddle.
Assistants: Dr. Steen Hansen, Dr. Troels Petersen, Dr. Stefania Xella.

Sponsored by:

The faculty of Natural Science (Copenhagen University)
Nordforsk
NBIA (Niels Bohr International Academy)
DARK (Dark Cosmology Centre)

Course Outline elite_phd_kursus_final.pdf

document Running_a_simulation_with_Gadget.pdf

Monday, 19 October

09:00 → 10:30 Basic Statistics

Mean, Variance, Standard Deviation. Gaussian Standard Deviation. Covariance, correlations. Basic distributions : Binomial, Poisson, Gaussian. Central Limit Theorem. Error propagation

Speaker: Dr Wouter Verkerke (Nikhef)

Slides data_analysis_2009_part1.pdf

10:30 → 11:00 coffe break/questions

11:00 → 12:30 Event Classification

Comparing discriminating variables. Choosing the optimal cut. Working in more than one dimension. Approximating the optimal discriminant. Techniques: Principal component analysis, Fisher Discriminant, Neural Network, Boosted Decision Trees, Probability Density Estimate, Empirical Modeling

Speaker: Dr Wouter Verkerke (Nikhef)

Slides data_analysis_2009_part2.pdf

13:30 → 17:30 computer exercises (Rockefeller)

Speakers: Dr Stefania Xella, Dr Troels Petersen, Dr Wouter Verkerke (Nikhef)

Tuesday, 20 October

09:00 → 10:30 Estimation and fitting

Introduction to estimation. Properties of chi-2, Maximum Likelihood estimators. Measuring and interpreting Goodness-Of-Fit. Numerical stability issues in fitting. Mitigating fit stability problems. Bounding fit parameters. Fit validation studies. Maximum Likelihood bias issues at low statistics. Toy Monte Carlo techniques. Designing and understanding Joint fits. Designing and understanding Multi-dimensional fits.

Speaker: Dr Wouter Verkerke (Nikhef)

Slides data_analysis_2009_part3.pdf

10:30 → 11:00 coffe break/questions

11:00 → 12:30 Confidence interval, limits & significance

Probability, Bayes Theorem. Simple Bayesian methods and issues. Frequentist confidence intervals and issues. Classical hypothesis testing. Goodness-of-fit. Likelihood ratio intervals and issues. Nuisance parameters. Likelihood principle

Speaker: Dr Wouter Verkerke (Nikhef)

Slides data_analysis_2009_part4.pdf

13:30 → 17:30 computer exercises (Rockefeller)

Speakers: Dr Stefania Xella, Dr Wouter Verkerke (Nikhef)

Wednesday, 21 October

09:00 → 10:30 Systematic Uncertainties

Sources of systematic errors. Sanity checks versus systematic error studies. Common issues in systematic evaluations. Correlations between systematic uncertainties. Combining statistical and systematic error

Speaker: Dr Wouter Verkerke (Nikhef)

Slides data_analysis_2009_part5.pdf

10:30 → 11:00 coffe break/questions

11:00 → 12:30 Models, physical laws and some cosmological background

This topic will introduce concepts of modelling that are to be studied later in the course, mainly in a general setting. In the latter part I will discuss some of the current issues in cosmology demanding advanced statistical treatments, in order to provide focus and motivate some examples that will be used during the course. Note however that most of the remaining course material will be applicable to a wide range of scientific discplines.

Speaker: Prof. Andrew Liddle (Sussex University)

Slides liddlelecture1.pdf

13:30 → 17:30 computer exercises (Rockefeller)

Speakers: Prof. Andrew Liddle (Sussex University), Dr Steen Hansen, Dr Stefania Xella, Dr Troels Petersen, Dr Wouter Verkerke (Nikhef)

Thursday, 22 October

09:00 → 10:30 Inference

A discussion of the underpinnings of statistical inference, particularly the methods of the Bayesian school. The different levels of Bayesian inference, parameter estimation and model selection, will be introduced.

Speaker: Prof. Andrew Liddle (Sussex University)

Slides liddlelecture2.pdf

10:30 → 11:00 coffe break/questions

11:00 → 12:30 Parameter estimation and Monte Carlo methods

Techniques for estimation of model parameters, likelihood analysis, Monte Carlo sampling methods, Metropolis-Hastings algorithm, machine learning.

Speaker: Prof. Andrew Liddle (Sussex University)

Slides liddlelecture3.pdf

13:30 → 17:30 computer exercises (Rockefeller)

Speakers: Prof. Andrew Liddle (Sussex University), Dr Steen Hansen

Examples for Thursday thursdayexamples.pdf

19:00 → 21:00 Dinner

Friday, 23 October

09:00 → 10:30 Model selection and multi-model inference

Techniques for comparison of competing models, model simplicity and predictiveness, Bayesian model selection, computational approaches to model selection, inference in the presence of model uncertainty (multi-model inference), non-Bayesian methods and information theory.

Speaker: Prof. Andrew Liddle (Sussex University)

Slides liddlelecture4.pdf

10:30 → 11:00 coffe break/questions

11:00 → 12:30 Forecasting and experimental design

Quantifying experimental capability, optimizing experimental capability, parameter estimation and model selection approaches to optimization.

Speaker: Prof. Andrew Liddle (Sussex University)

Slides liddlelecture5.pdf

13:30 → 17:00 computer exercises (Rockefeller)

Speakers: Prof. Andrew Liddle (Sussex University), Dr Steen Hansen

Datafile 1 for Problem 2 (x,y,sigma) dataset1.dat

Datafile 2 for Problem 2 (x,y,sigma) dataset2.dat

Examples for Friday fridayexamples.pdf