Bayesian inference of scaled versus fractional Brownian motion
Samudrajit Thapa, Seongyu Park, Yeong-Jin Kim, Jae‐Hyung Jeon, Ralf Metzler, Michael A. Lomholt
Abstract
Abstract We present a Bayesian inference scheme for scaled Brownian motion, and investigate its performance on synthetic data for parameter estimation and model selection in a combined inference with fractional Brownian motion. We include the possibility of measurement noise in both models. We find that for trajectories of a few hundred time points the procedure is able to resolve well the true model and parameters. Using the prior of the synthetic data generation process also for the inference, the approach is optimal based on decision theory. We include a comparison with inference using a prior different from the data generating one.
Topics & Concepts
InferenceFractional Brownian motionBayesian inferenceBayesian probabilityFiducial inferenceFrequentist inferenceBrownian motionComputer scienceStatistical inferenceMathematicsAlgorithmArtificial intelligenceStatistical physicsStatisticsPhysicsFractional Differential Equations SolutionsAdvanced Statistical Methods and ModelsControl Systems and Identification