Bayesian statistics

Bayesian statistics 478 How Bayesian methods work 480 Prior distributions 482 Likelihood; posterior distributions 484 Summarizing and presenting results 486 Using Bayesian analyses in medicine 488 Software for Bayesian statistics 492 Reading Bayesian analyses in papers 494 Bayesian methods: a summary 496 In this chapter we describe the Bayesian approach to statistical analysis in contrast to the frequentist approach. We describe how Bayesian methods work including a description of prior and posterior distributions. We outline the role and choice of prior distributions and how they are combined with the data collected to provide an updated estimate of the unknown quantity being studied. We include examples of the use of Bayesian methods in medicine, and discuss the pros and cons of the Bayesian approach compared with the frequentist approach Finally, we give guidance on how to read and interpret Bayesian analyses in the medical literature....