Parameter estimation and uncertainty quantification using information geometry
J.A. Sharp, Alexander P. Browning, Kevin Burrage, Matthew J. Simpson
Abstract
In this work, we: (i) review likelihood-based inference for parameter estimation and the construction of confidence regions; and (ii) explore the use of techniques from information geometry, including geodesic curves and Riemann scalar curvature, to supplement typical techniques for uncertainty quantification, such as Bayesian methods, profile likelihood, asymptotic analysis and bootstrapping. These techniques from information geometry provide data-independent insights into uncertainty and identifiability, and can be used to inform data collection decisions. All code used in this work to implement the inference and information geometry techniques is available on GitHub.
Topics & Concepts
GeodesicComputer scienceCurvatureInferenceInformation geometryUncertainty quantificationBayesian probabilityMathematicsAlgorithmGeometryMachine learningArtificial intelligenceScalar curvatureMarkov Chains and Monte Carlo MethodsBayesian Modeling and Causal InferenceStatistical Methods and Inference