Quantifying Uncertainty in the Estimation of Probability Distributions

Jimena Davis, North Carolina State University

We will discuss an inverse problem computational methodology for the estimation of functional parameters in the presence of (model and data) uncertainty. We consider a class of inverse problems in which the underlying dynamics are described by partial differential equations and the unknown parameter of interest is a probability distribution describing the variability of growth rates across a size-structured population. Computationally efficient approximation methods for both parametric and non-parametric versions of an ordinary least squares (OLS) inverse problem are developed to address the infinite-dimensional nature of both the state and parameter space. We will also demonstrate how to construct “functional” confidence bands that will aid in quantifying the uncertainty in estimated probability distributions by using the standard asymptotic theory for finite dimensional OLS estimators. Computational and statistical results for the estimation of growth rate distributions in size-structured marine populations are presented to illustrate the strengths and weaknesses associated with these methods.

Abstract Author(s): Jimena L. Davis and H.T. Banks