Statistics and Data Analysis
The aim of this 3-day online course, to acquire the skills needed for analysis of experimental data and model fitting.
Objectives:
At the end of this course, a successful student will be able to:
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Understand the basis of Bayesian analysis of data, including marginalisation.
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Understand the principles of sampling of distributions, especially MCMC.
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Have written an MCMC code to sample Bayesian posterior distributions, incorporating known priors on the model parameters.
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Appreciate the need for, and be able to interpret, convergence tests.
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Understand Bayesian Hierarchical Modelling and Simulation-based inference.
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Be able to simulate (parts of) an experiment or model, in order to test analysis code.
Prerequisites:
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/); a programming language of choice (we expect this to be Python in most cases).
Online Course Structure (provisional):
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.
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Day 1 - Introduction to Bayes theorem for inference, priors, sampling distributions, likelihoods and posterior probabilities. Marginalisation.
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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.