Abstract
Bayesian statistics is not just the application of Bayes theorem within statistics, that is ubiquitous anyway. Rather it is a whole style of thinking that leads to different forms of statistical testing and estimation. This chapter examines the 'job of statistics': obtaining uncertain understanding of the unknown world through probabilistic measurements. We see how traditional statistics and Bayesian statistics address this fundamental uncertainty in different ways; in particular, Bayesian statistics is fundamentally reasoning about our beliefs encoded as if they were probabilities. This can be incredibly powerful, but, like driving a Porsche, also potentially dangerous. The chapter introduces you to some of the techniques of Bayesian statistics for testing hypotheses, estimating values, and creating credible intervals as ways of expressing range of uncertainty. It also aims to help you dispel some of the hype, avoid some of the pitfalls and learn when it is the right tool for the job.
Keywords:statistics, Bayes theorem, Bayes factor, statistical crisis, credible interval, cherry picking, human-computer interaction
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