Bayesian Inference Frameworks for Fluorescence Microscopy Data Analysis In this work, I present a Bayesian inference computational framework for the analysis of widefield microscopy data that addresses three challenges: (1) counting and localizing stationary fluorescent molecules; (2) inferring a spatially-dependent effective fluorescence profile that describes the spatially-varying rate at which fluorescent molecules emit subsequently-detected photons (due to different illumination intensities or different local environments); and (3) inferring the camera gain. My general theoretical framework utilizes the Bayesian nonparametric Gaussian and beta-Bernoulli processes with a Markov chain Monte Carlo sampling scheme, which I further specify and implement for Total Internal Reflection Fluorescence (TIRF) microscopy data, benchmarking the method on synthetic data. These three frameworks are self-contained, and can be used concurrently so that the fluorescence profile and emitter locations are both considered unknown and, under some conditions, learned simultaneously. The framework I present is flexible and may be adapted to accommodate the inference of other parameters, such as emission photophysical kinetics and the trajectories of moving molecules. My TIRF-specific implementation may find use in the study of structures on cell membranes, or in studying local sample properties that affect fluorescent molecule photon emission rates.autWallgren, RossthsPresse, StevethsArmbruster, HansdgcMcCulloch, RobertpblArizona State UniversityengPartial requirement for: M.A., Arizona State University, 2019Includes bibliographical references (pages 32-36)Field of study: Applied mathematicsby Ross Wallgrenhttps://hdl.handle.net/2286/R.I.5354500Masters ThesisAcademic thesesiv, 64 pages : illustrations (some color)115579411351630032421157121systemIn Copyright2019TextMathematicsStatisticsBiophysicsBayesianbeta-bernoulli processgaussian processMarkov Chain Monte CarloMicroscopysuperresolutionFluorescence microscopy--Mathematical models.Fluorescence MicroscopyBayesian statistical decision theory--Scientific applications.Bayesian statistical decision theory