Advancing Biophysics Research with Bayesian Methods: Novel Applications and Insights into Biological Systems' Behavior

The Bayesian paradigm provides a flexible and versatile framework for modeling complex biological systems without assuming a fixed functional form or other constraints on the underlying data. This dissertation explores the use of Bayesian nonparametric methods for analyzing fluorescence microscopy data in biophysics, with a focus on enumerating diffraction-limited particles, reconstructing potentials from trajectories corrupted by measurement noise, and inferring potential energy landscapes from fluorescence intensity experiments. This research demonstrates the power and potential of Bayesian methods for solving a variety of problems in fluorescence microscopy and biophysics more broadly.