A Bayesian Approach for the Determination of the Charge Density from Elastic Electron Scattering Data

Details A Bayesian Approach for the Determination of the Charge Density from Elastic Electron Scattering Data A Bayesian Approach for the Determination of the Charge Density from Elastic Electron Scattering Data

2001-11-14

arxiv.org/abs/physics/0111119v1

Physics

Data Analysis, Statistics and Probability

Presented at MaxEnt97. Appeared in Maximum Entropy and Bayesian Methods, G.J. Erickson, J.T. Rychert and C.R. Smith (Ed.), Klu

Scientific paper

The problem of the determination of the charge density from limited information about the charge form factor is an ill-posed inverse problem. A Bayesian probabilistic approach to this problem which permits to take into account both errors and prior information about the solution is presented. We will show that many classical methods can be considered as special cases of the proposed approach. We address also the problem of the basis function choice for the discretization and the uncertainty of the solution. Some numerical results for an analytical model are presented to show the performance of the proposed method.

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