Practical Bayesian Inference in Neuroscience: Or How I Learned To Stop Worrying and Embrace the Distribution

Abstract

Typical statistical practices in biological sciences have been increasingly called into question due to difficulties in replication of an increasing number of studies, much of which is confounded by the relative difficulty of null significance hypothesis testing designs and interpretation of p-values. Bayesian inference, representing a fundamentally different approach to hypothesis testing, is receiving renewed interest as a potential alternative or complement to traditional null significance hypothesis testing due to its ease of interpretation and explicit declarations of prior assumptions. Bayesian models are more mathematically complex than equivalent frequentist approaches, which have historically limited applications to simplified analysis cases. However, the advent of probability distribution sampling tools with exponential increases in computational power now allows for quick and robust inference under any distribution of data. Here we present a practical tutorial on the use of Bayesian inference in the context of neuroscientific studies. We first start with an intuitive discussion of Bayes’ rule and inference followed by the formulation of Bayesian-based regression and ANOVA models using data from a variety of neuroscientific studies. We show how Bayesian inference leads to easily interpretable analysis of data while providing an open-source toolbox to facilitate the use of Bayesian tools.Significance StatementBayesian inference has received renewed interest as an alternative to null-significance hypothesis testing for its interpretability, ability to encapsulate prior knowledge into current inference, and robust model comparison paradigms. Despite this renewed interest, discussions of Bayesian inference are often obfuscated by undue mathematical complexity and misunderstandings underlying the Bayesian inference process. In this article, we aim to empower neuroscientists to adopt Bayesian statistical inference by providing a practical methodological walkthrough using single and multi-unit recordings from the rodent auditory circuit accompanied by a well-documented and user-friendly toolkit containing regression and ANOVA statistical models commonly encountered in neuroscience.

Characterization and closed-loop control of infrared thalamocortical stimulation produces spatially constrained single-unit responses

“…S1–S9 ). Bayesian inference estimates the distribution of likely regression parameters from observed data ( 78 ). Regression parameters were summarized by their maximum a priori estimate(MAP) (i.e.…”