Bringing Bayes and Shannon to the Study of Behavioural and Neurobiological Timing and Associative Learning

Bayesian parameter estimation and Shannon's theory of information provide tools for analysing and understanding data from behavioural and neurobiological experiments on interval timing-and from experiments on Pavlovian and operant conditioning, because timing plays a fundamental role in associative learning. In this tutorial, we explain basic concepts behind these tools and show how to apply them to estimating, on a trial-by-trial, reinforcement-by-reinforcement and response-by -response basis, important parameters of timing behaviour and of the neurobiological manifesta-tions of timing in the brain. These tools enable quantification of relevant variables in the trade-off between acting as an ideal observer should act and acting as an ideal agent should act, which is also known as the trade-off between exploration (information gathering) and exploitation (information utilization) in reinforcement learning. They enable comparing the strength of the evidence for a measurable association to the strength of the behavioural evidence that the association has been perceived. A GitHub site and an OSF site give public access to well-documented Matlab and Python code and to raw data to which these tools have been applied.