*Section author: Danielle J. Navarro and David R. Foxcroft*

# Bayesian statistics¶

In our reasonings concerning matter of fact, there are all imaginable degrees of assurance, from the highest certainty to the lowest species of moral evidence. A wise man, therefore, proportions his belief to the evidence.

The ideas I’ve presented to you in this book describe inferential
statistics from the frequentist perspective. I’m not alone in doing
this. In fact, almost every textbook given to undergraduate psychology
students presents the opinions of the frequentist statistician as *the*
theory of inferential statistics, the one true way to do things. I have
taught this way for practical reasons. The frequentist view of
statistics dominated the academic field of statistics for most of the
20th century, and this dominance is even more extreme among applied
scientists. It was and is current practice among psychologists to use
frequentist methods. Because frequentist methods are ubiquitous in
scientific papers, every student of statistics needs to understand those
methods, otherwise they will be unable to make sense of what those
papers are saying! Unfortunately, in my opinion at least, the current
practice in psychology is often misguided and the reliance on
frequentist methods is partly to blame. In this chapter I explain why I
think this and provide an introduction to Bayesian statistics, an
approach that I think is generally superior to the orthodox approach.

This chapter comes in two parts: In sections Probabilistic reasoning by rational agents through Why be a Bayesian? I talk about what Bayesian statistics are all about, covering the basic mathematical rules for how it works as well as an explanation for why I think the Bayesian approach is so useful. Afterwards, I provide a brief overview of how you can do Bayesian versions of t-tests.