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Advanced methods in statistical data analysis

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

Aud A (Blegdamsvej) mornings - Canteen (Rockefeller) afternoons. Friday Rockecfeller (auditorium + canteen) all day
Description
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
document
  • Monday 19 October
    • 1
      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
    • 2
      coffe break/questions
    • 3
      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
    • 4
      computer exercises (Rockefeller)
      Speakers: Dr Stefania Xella, Dr Troels Petersen, Dr Wouter Verkerke (Nikhef)
  • Tuesday 20 October
    • 5
      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
    • 6
      coffe break/questions
    • 7
      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
    • 8
      computer exercises (Rockefeller)
      Speakers: Dr Stefania Xella, Dr Wouter Verkerke (Nikhef)
  • Wednesday 21 October
    • 9
      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
    • 10
      coffe break/questions
    • 11
      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
    • 12
      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
    • 13
      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
    • 14
      coffe break/questions
    • 15
      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
    • 16
      computer exercises (Rockefeller)
      Speakers: Prof. Andrew Liddle (Sussex University), Dr Steen Hansen
      Examples for Thursday
    • 17
      Dinner
  • Friday 23 October
    • 18
      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
    • 19
      coffe break/questions
    • 20
      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
    • 21
      computer exercises (Rockefeller)
      Speakers: Prof. Andrew Liddle (Sussex University), Dr Steen Hansen
      Datafile 1 for Problem 2 (x,y,sigma)
      Datafile 2 for Problem 2 (x,y,sigma)
      Examples for Friday
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