To Bayes, or Not to Bayes, Information is the Answer

Abstract

Biological systems are inherently noisy on a molecular scale. The problem of determining the true state of a system and characterizing the transitions between states whose observables are corrupted by noise is a canonical problem in statistics with a rich history. There has recently been a significant renaissance in the application of Bayesian Statistics (for instance variational Bayes and the use of the Bayesian Information Criterion) to analyze single-molecule biophysics and cell-biology problems. Although these Bayesian techniques regularize the model selection problem to prevent over-fitting through the introduction of a prior probability distribution, Bayesian techniques typically significantly underestimate the complexity that can be resolved by information-based and frequentist analyses and often require the introduction of ad hoc prior distributions. We demonstrate the application of information-based statistics (both canonical and novel) in the analyses of several distinct biological measurements from our laboratory ranging from single-molecule techniques including stoichiometry by bleaching and tether-particle motion to cell biology problems including characterizing cell motility. In each case we compare the resolution of the Bayesian and information-based approaches to demonstrate the increased resolving power of information-based techniques.