In the modern world we must often make decisions under uncertainty, weighing up our options in the face of incomplete (and often conflicting) information. In this unit we examine the problems of evaluating evidence, forming beliefs, and making decisions based on those beliefs. We do this through the lens of Bayesianism, an intuitive view of the world that considers all beliefs and evidence to have some level of uncertainty and subjectivity.

As both a philosophical approach and an explicit mathematical system, Bayesianism is increasingly being used in real world problems across many fields. Using Bayesian approaches to deal with uncertainty is becoming essential to not only the physical and social sciences, but also to applied disciplines such as economics, marketing, law, engineering, IT, medicine and nursing. For example, what should we believe about our health based on the result of a medical test, and what treatment option, if any, should we choose? How should we evaluate evidence for climate change and what policies should we support to deal with its potential consequences? Through a Bayesian approach we can use simple arithmetic to quantify our uncertainty about the evidence, update our beliefs from that evidence, and decide on a course of action - even when there may be no single or "right" course of action.

By understanding the components of Bayesian inference, along with applications of Bayes rule to real world problems, we help students to think more deeply about how they make decisions, why they make the decisions they do, and ultimately how to make better decisions.