APPLIED MATHEMATICS, INC. — Department of Defense STTR Phase I: Mathematical models of physical and biological systems contain parameters that need to be

Description

Mathematical models of physical and biological systems contain parameters that need to be estimated from measured data. Models with parameters distributed probabilistically require the estimates of a probability measure over the set of admissible parameters. We propose to use frequentist-based approaches for non-parametrically estimating probability measures that describe the distribution of parameters across all members of a given population in the case where only aggregate longitudinal data are available. We will investigate least squares method combined with delta function approximation methods or linear spline approximation methods or other plausible approximation methods in order to achieve the convergence required for near real-time estimation. Project tasks are to survey existing techniques and select non-Bayesian candidate methods for near-real-time estimation of probabilistic parameters; develop theoretical and computational ideas to validate capability for describing near-real-time parameters; develop general methodology for near-real-time quantification of stochastic model parameters; analyze proposed methodology to include bias and convergence properties of estimators; conduct proof-of-concept 3D computations of the proposed methodology; and prepare final report and periodic progress reports.