The effects of parametrization on inverse problems
نویسندگان
چکیده
We consider two example systems, a logistic-growth population model and a damped spring-mass model. These models are each parameterized in two different ways. In one case (the logistic) the parameters are independent in one formulation and dependent in the other. In the other example (the spring-mass), the parameterizations are each independent. We carry out a series of inverse problems for these examples using ordinary least squares on each model. We use uncertainty quantification methods involving asymptotic theory to investigate for evidence of parameter dependence. We examine the off-diagonal elements of the Fisher Information (covariance) matrix to compare the matrices created by dependent and independent parametrizations. We further compare the use of exact vs. asymptotic confidence ellipsoids. Finally we compare the confidence ellipsoids generated by asymptotic theory to those created using Monte Carlo simulations.
منابع مشابه
Inverse and Reverse 2-facility Location Problems with Equality Measures on a Network
In this paper we consider the inverse and reverse network facility location problems with considering the equity on servers. The inverse facility location with equality measure deals with modifying the weights of vertices with minimum cost, such that the difference between the maximum and minimum weights of clients allocated to the given facilities is minimized. On the other hand, the reverse c...
متن کاملSolving Inverse Sturm-Liouville Problems with Transmission Conditions on Two Disjoint Intervals
In the present paper, some spectral properties of boundary value problems of Sturm-Liouville type on two disjoint bounded intervals with transmission boundary conditions are investigated. Uniqueness theorems for the solution of the inverse problem are proved, then we study the reconstructing of the coefficients of the Sturm-Liouville problem by the spectrtal mappings method.
متن کاملA numerical Algorithm Based on Chebyshev Polynomials for Solving some Inverse Source Problems
In this paper, two inverse problems of determining an unknown source term in a parabolic equation are considered. First, the unknown source term is estimated in the form of a combination of Chebyshev functions. Then, a numerical algorithm based on Chebyshev polynomials is presented for obtaining the solution of the problem. For solving the problem, the operational matrices of int...
متن کاملThe uniqueness theorem for inverse nodal problems with a chemical potential
In this paper, an inverse nodal problem for a second-order differential equation having a chemical potential on a finite interval is investigated. First, we estimate the nodal points and nodal lengths of differential operator. Then, we show that the potential can be uniquely determined by a dense set of nodes of the eigenfunctions.
متن کاملMinimum support nonlinear parametrization in the solution of a 3D magnetotelluric inverse problem
In this paper we describe a new approach to shar p boundary geophy sical inversion. We demon strate that regularized inversion with a minimum support stabilizer can be implemented by using a specially designed nonl inear parametrization of the mode l parameters . Thi s parametrization plays the same role as transformation into the space of the weighted model parameters, introd uced in the origi...
متن کاملParametrization of Pedestrian Injuries and its Utilisation in Proving Traffic Accidents Course Using Injury Signatures and Contact Signatures
Background: The paper points out the present limited possibility of using the verbal description of injuries for the needs of experts from the field of road transportation as relevant criminalistics traces, as well as the options of the FORTIS system that creates a new area for a deeper interdisciplinary approach in the field of expert evidence. Further a description of how to create injury si...
متن کامل