Plausible Reasoning in Neuroscience

What is probability? How this relate to statistical inference? These are fundamental questions, the answer to which varies greatly, depending on the approach adopted. This chapter takes the perspective of the Bayesian tradition, describing the differences with the canonical frequentist one. By discussing the logical and mathematical foundations of probability introduced by Cox and Jaynes, it will be shown how the early objections to the Bayesian approach can be overcome. Next, it will be highlighted how the Bayesian approach offers a useful method to deal with the choice of research hypotheses. Several examples of parameters estimation and model comparison will be described, whose solutions are based on distributions of probabilities, previously introduced. Some relevant Bayesian theories from neuroscientific literature, such as multimodal sensory integration and predictive coding, will be described. Finally, an application to neuroimaging meta-analytical methods will be presented.