Narrow Results

In this paper we present a method for the estimation of the parameters of models described by a nonlinear system of differential equations: we study the maximum likelihood estimator and the jackknife estimator for parameters of the system and for the covariance matrix of the state variables and we seek possible linear relations between parameters. We take into account the difficulty due to the small number of observations. The optimal experimental design for this kind of problem is determined. We give an application of this method for the glucose metabolism of goats.

This tutorial demonstrates the use of information geometry tools in analyzing environmental parameter sensitivities in underwater acoustics. Sensitivity analyses quantify how well data can constrain model parameters, with application to inverse problems like geoacoustic inversion. A review of examples of parameter sensitivity methods and their application to problems in underwater acoustics is given, roughly grouped into “local” and “non-local” methods. Local methods such as Fisher information and Cramér-Rao bounds have important connections to information geometry. Information Geometry combines the fields of information theory and differential geometry by interpreting a model as a Riemannian manifold, known as the model manifold, that encodes both local and global parameter sensitivities. As an example, 2-dimensional model manifold slices are constructed for the Pekeris waveguide with sediment attenuation, for a vertical array of hydrophones. This example demonstrates how effective, reduced-order models emerge in certain parameter limits, which correspond to boundaries of the model manifold. This example also demonstrates how the global structure of the model manifold influences the local sensitivities quantified by the Fisher information matrix. This paper motivates future work to utilize information geometry methods for experimental design and model reduction applied to more complex modeling scenarios in underwater acoustics.