Basic Statistics

• Wouter Verkerke (Nikhef)

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

coffe break/questions

Event Classification

• Wouter Verkerke (Nikhef)

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

computer exercises (Rockefeller)

• Wouter Verkerke (Nikhef)
• Troels Petersen
• Stefania Xella

Estimation and fitting

• Wouter Verkerke (Nikhef)

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.

coffe break/questions

Confidence interval, limits & significance

• Wouter Verkerke (Nikhef)

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

computer exercises (Rockefeller)

• Wouter Verkerke (Nikhef)
• Stefania Xella

Systematic Uncertainties

• Wouter Verkerke (Nikhef)

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

coffe break/questions

Models, physical laws and some cosmological background

• Andrew Liddle (Sussex University)

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.

computer exercises (Rockefeller)

• Steen Hansen
• Andrew Liddle (Sussex University)
• Wouter Verkerke (Nikhef)
• Troels Petersen
• Stefania Xella

Inference

• Andrew Liddle (Sussex University)

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.

coffe break/questions

Parameter estimation and Monte Carlo methods

• Andrew Liddle (Sussex University)

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

computer exercises (Rockefeller)

• Steen Hansen
• Andrew Liddle (Sussex University)

Dinner

Model selection and multi-model inference

• Andrew Liddle (Sussex University)

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.

coffe break/questions

Forecasting and experimental design

• Andrew Liddle (Sussex University)

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

computer exercises (Rockefeller)

• Steen Hansen
• Andrew Liddle (Sussex University)