Bayesian inference in FMRI

Bayesian inference has taken FMRI methods research into areas that frequentist statistics have struggled to reach. In this article we will consider some of the early forays into Bayes and what motivated its use. We shall see the impact that Bayes has had on haemodynamic modelling, spatial modelling, group analysis, model selection and brain connectivity analysis; and consider how these advancements have spun-off into related areas of neuroscience and some of the challenges that remain. Bayes has brought to the table inference flexibility, incorporation of prior information, adaptive regularisation and model selection. But perhaps more important than these things, is the ability of Bayes to empower the methods researcher with a mathematically principled framework for inferring on any model.