Day 1-3 lecturer: Dr. W. Verkerke
1) Basic Statistics
Mean, Variance, Standard Deviation. Gaussian Standard Deviation. Covariance, correlations. Basic distributions : Binomial, Poisson, Gaussian. Central Limit Theorem. Error propagation
2) 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
3) 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.
4) 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
5) 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 and problem-solving.
Day 3-5 lecturer: Dr. R. Trotta
1. Foundational aspects: what is probability?
Probability as frequency; Probability as degree of knowledge; Bayes Theorem; Priors; Building the likelihood function; Combination of multiple observations; Nuisance parameters
2. Learning from experience: Bayesian parameter inference
Markov Chain Monte Carlo methods; Importance sampling; Nested sampling; Reporting inferences; Credible regions vs confidence regions; The meaning of sigma
3. Bayesian model selection and cosmological applications
The different levels of inference; The Bayesian evidence and the Bayes factor; Computing Bayes factors; Information criteria for approximate model selection; The meaning of significance; Comparison with classical hypothesis testing; Model complexity; Bayesian model averaging
4. Experiment optimization and prediction
Fisher matrix formalism; Figures of merit; Expected usefulness of an experiment ; Survey optimization; Experimental utility; Bayesian adaptive exploration; Applications to dark energy
1) Basic Statistics
Mean, Variance, Standard Deviation. Gaussian Standard Deviation. Covariance, correlations. Basic distributions : Binomial, Poisson, Gaussian. Central Limit Theorem. Error propagation
2) 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
3) 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.
4) 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
5) 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 and problem-solving.
Day 3-5 lecturer: Dr. R. Trotta
1. Foundational aspects: what is probability?
Probability as frequency; Probability as degree of knowledge; Bayes Theorem; Priors; Building the likelihood function; Combination of multiple observations; Nuisance parameters
2. Learning from experience: Bayesian parameter inference
Markov Chain Monte Carlo methods; Importance sampling; Nested sampling; Reporting inferences; Credible regions vs confidence regions; The meaning of sigma
3. Bayesian model selection and cosmological applications
The different levels of inference; The Bayesian evidence and the Bayes factor; Computing Bayes factors; Information criteria for approximate model selection; The meaning of significance; Comparison with classical hypothesis testing; Model complexity; Bayesian model averaging
4. Experiment optimization and prediction
Fisher matrix formalism; Figures of merit; Expected usefulness of an experiment ; Survey optimization; Experimental utility; Bayesian adaptive exploration; Applications to dark energy
