An introduction to Bayesian methods for analyzing chemistry data: Part 1: An introduction to Bayesian theory and methods

In this tutorial paper, we outline the application of Bayesian theory and methods for analysing experimental chemistry data. We provide an overview of the background theory and the essential rules necessary for manipulating conditional probabilities and density functions (pdfs) i.e. the product and marginalisation rules. Drawing on these rules we demonstrate, using a variety of examples from chemistry, how Bayes theorem can be adapted to analyse and interpret experimental data for a wide range of typical chemistry experiments, including basic model selection (i.e. hypothesis testing), parameter estimation, peak refinement and advanced model selection. An outline of the steps and underlying assumptions are presented, while necessary mathematics are also discussed.