A primer on Bayesian inference for biophysical systems.

Area of Science:

• Biophysics
• Statistical Modeling
• Computational Science

Background:

• Bayesian inference is a widely adopted statistical paradigm across scientific disciplines.
• Its application in biophysics has been less prevalent compared to other fields.
• This tutorial aims to bridge this gap by providing accessible explanations and examples relevant to biophysicists.

Purpose of the Study:

• To provide an accessible tutorial on Bayesian inference methods for biophysicists.
• To illustrate the application of Bayesian methods using examples familiar to the biophysics community.
• To demonstrate the utility of Markov chain Monte Carlo (MCMC) sampling for complex model parameter inference.

Main Methods:

• Introduction to the fundamental concepts of Bayesian inference.
• Explanation of posterior inference using conjugate priors with simple examples.
• Detailed description of Markov chain Monte Carlo (MCMC) sampling algorithms, including Gibbs sampling and Metropolis random walk.
• Application of these methods to biophysics-relevant problems.

Main Results:

• Demonstration of how Bayesian inference can be applied to biophysical problems.
• Illustrative examples of posterior inference using conjugate priors.
• Practical guidance on implementing Gibbs sampling and Metropolis random walk algorithms.
• Showcasing the generalizability of Bayesian methods with MCMC for complex model parameter inference and identifiability.

Conclusions:

• Bayesian inference, coupled with MCMC sampling, offers a robust framework for parameter inference in biophysics.
• These methods provide a generalizable approach to rigorously analyze arbitrarily complicated biophysical models.
• The tutorial aims to facilitate wider adoption of Bayesian techniques within the biophysics field.