Introduction to Bayesian Statistics using R

Overview

Bayesian statistics have become very popular in recent years. Modern software has made this possible and Bayesian methods are now applied in a wide range of scientific application areas from medicine to ecology. This course provides an introduction to the motivation, methods and applications of Bayesian statistics. The analysis tool is R; prior knowledge of this software is assumed.

The course is a mixture of presentations and hands-on computer exercises. It begins with an overview of the rationale and methodology underpinning Bayesian analysis, and the Markov chain Monte Carlo (MCMC) computational tools behind the methodology are outlined. An introduction to the JAGS engine within the R software is then provided, followed by data analysis applications, including linear models and generalised linear models. The advantages of Bayesian approach applied to the latter are emphasised and considered in detail. For example, the question “What is the chance that method A better than method B?” can be easily addressed in a Bayesian framework, but not in classical statistics.

The emphasis in this course is on practical data analysis, although the essential theory will be outlined. Examples are drawn from a range of scientific disciplines.

Duration

2 days

Delivery Mode

All training is online and will be delivered live each day between 09:00 and 17:30 (GMT+1). Delivery platform: Zoom, which may be freely accessed. Questions may be asked using Zoom's chat box. Note our online courses are delivered by a team of two presenters, meaning at least one presenter is always available to provide additional support. During presentations, the team member who is not speaking can take questions in addition to the presenter.

Who Should Attend?

Data analysts and statisticians who want an introduction to Bayesian methods for statistical analysis. No prior knowledge of Bayesian statistics is required. Participants are expected to have:

• An A-level mathematics qualification or equivalent, including knowledge of probability density functions and probability mass functions for describing distributions
• A working knowledge of linear models and generalised linear models
• A working knowledge of the R statistics software.

How You Will Benefit

By the end of the course you will have a firm understanding of Bayesian methods and their flexibility. You will also have acquired a working knowledge of specialised software for Bayesian data analysis and will be able to fit and interpret linear and generalised linear models in a Bayesian framework. You will also appreciate the practical benefits of Bayesian methods.

What Do We Cover?

• Bayesian versus classical frequentist statistics
• Likelihood, prior and posterior distributions and the use of Bayes' theorem
• Bayesian analysis of single-parameter models and multi-parameter models
• Conjugate, vague and informative priors
• Simulation of posterior distributions; posterior summaries
• Markov chain Monte Carlo (MCMC) methods and MCMC diagnostics
• Linear models, generalised linear models and model selection
• Questions that classical statistics find difficult to answer or cannot answer
• Use of the JAGS software via R and the CRAN packages rjags, runjags and coda.

Software

Practical work will be done in R.

Note: For practical work, participants must download and install (i) the JAGS software and (ii) a number of CRAN packages in R. This must be done prior to the start of the course.