A very simple introduction to Bayesian statistics: From coin flips to insight

Bayesian statistical analyses are a growing part of the chemical and biological sciences for several reasons. Most importantly, the Bayesian approach of predicting underlying models based on data corresponds naturally with examination of complex systems, whether using wet-lab or computational means. The Bayesian structure also provides a systematic basis for estimating uncertainty in model parameters and permits incorporation of prior information in a quantitative and consistent way. While easy to state in words, these strengths of Bayesian analysis can be difficult to assimilate for beginners. This short article presents essential Bayesian concepts using very simple examples and the absolute minimum mathematics needed to maintain rigor.