Statistics and Data Analysis

Objectives:

At the end of this course, a successful student will be able to:

​

1. Understand the basis of Bayesian analysis of data, including marginalisation.

2. Understand the principles of sampling of distributions, especially MCMC.

3. Have written an MCMC code to sample Bayesian posterior distributions, incorporating known priors on the model parameters.

4. Appreciate the need for, and be able to interpret, convergence tests.

5. Understand Bayesian Hierarchical Modelling and Simulation-based inference.

6. Be able to simulate (parts of) an experiment or model, in order to test analysis code.

Course Structure:

Each day will comprise introductory lectures in the morning (10:00-11:00, 11:30-12:30) and practical exercises in the afternoons (13:30-17:30), inferring parameters from one example from gravitational physics, Higgs boson data, or supernova data.

​

Day 1 - Introduction to Bayes theorem for inference, priors, sampling distributions, likelihoods and posterior probabilities. Marginalisation.

​

Day 2 - Introduction to sampling; Monte Carlo Markov Chain (MCMC) principles; detailed balance; Metropolis-Hastings algorithm; Hamiltonian Monte Carlo.

 

​Day 3 - Bayesian Hierarchical Models; latent variables; Simulation-based inference.