An Inverse Problem Statistical Methodology Summary

Sensitivity equations for a size-structured population model

“…Suppose that the functions φ and Ψ in equation (8) are both dependent on the parameter θ in a convex subset Θ of some topological space. Then equation (8) becomes…”

“…However, to the best of our knowledge, thus far there is no literature on sensitivity equations and the related analysis for size-structured population models. Sensitivity analysis of dynamical systems has drawn the attention of numerous researchers [1,6,9,10,11,13,14,15,16,17,20,24,25,27,28,35,38,40] for many years because the resulting sensitivity functions can be used in many areas such as optimization and design [16,26,27,34,38], computation of standard errors [9,10,19,21,36], and information theory [12] related quantities (e.g., the Fisher information matrix) as well as control theory, parameter estimation and inverse problems [5,8,9,10,11,40,41]. One of our motivations for investigating sensitivity for size-structured population models derives from our efforts reported in [7], where a shrimp biomass production system and a…”

Estimation in time-delay modeling of insecticide-induced mortality

“…We do this in the context of a generalized least squares (GLS) inverse problem formulation which is appropriate when dealing with data containing relative noise (see the discussions in [7]). This type of data is frequently encountered when the data involves population counts (e.g., the error in counting 10 individuals vs. that in counting 1000 is likely to depend on the level of the count itself).…”

“…We then calculate an estimateΘ of the true parameters Θ 0 using a generalized least squares (GLS) procedure, which for our problem involves finding solutionsΘ to the normal equations (see [7] for a more detailed discussion)…”

“…The generalized least squares (GLS) procedure involves an iterative algorithm that consists of minimizing steps even though the GLS is not a minimization procedure (again see [7] for details).…”