Statistics and Data Analysis
This 3 day module will run on 14th, 16th and 18th June 2021. The module will be delivered on-line.
Each day will comprise intro lectures in the morning (1000-1100, 1130-1230) and practical exercises in the afternoons (1330-1730).
Day 1 Introduction to the methods of maximum likelihood and least-squares. Bayes theorem, priors and a posteriori probabilities. Goodness of fit: chi squared test, likelihood ratio, Bayesian evidence.
Day 2 Monte Carlo methods: simulations in particle physics and astronomy. Markov Chain Monte Carlo (MCMC): exploring a multi-dimensional parameter space using emcee.
Day 3 Model fitting: dealing with outliers, errors on 'independent' variable, intrinsic scatter in fitted model. Bayesian Hierarchical Models: introduction of latent variables to parametrize unknowns in the problem.
To acquire the skills needed for analysis of experimental data and model fitting.
At the end of this course, a successful student will be able to:
Fit models to data using maximum likelihood and least squares, incorporating known priors on the model parameters;
Assess the model goodness of fit, and obtain the covariance matrix of fitted parameters;
Be able to simulate (parts of) an experiment or model, in order to test analysis code;
Fit Bayesian hierarchical models to data, allowing marginalisation over unknown nuisance parameters.
Prerequisites / Linked Modules
Students should have previous familiarity with basic probability and be reasonably competent in Python scripting.
It is recommended that students have the following software installed on their laptops: Anaconda python distribution (https://www.anaconda.com/download/) emcee, affine-invariant MCMC code (http://dfm.io/emcee/current/)