@MISC{An_geometryof, author = {Or Azm An and A. P Azman}, title = {Geometry Of The Nonlinear Regression With Prior}, year = {} }

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Abstract

. In a nonlinear regression model with a given prior distribution, the estimator maximizing the posterior probability density is considered (a certain kind of Bayes estimator). It is shown that the prior influences essentially, but in a comprehensive way, the geometry of the model, including the intrinsic curvature measure of nonlinearity which is derived in the paper. The obtained geometrical results are used to present the modified Gauss-Newton method of computation of the estimator, and to obtain the exact and an approximate probability density of the estimator. 1. Introduction We consider the nonlinear regression model y = j(#) + "; (# 2 \Theta) " N(0; \Sigma) ; (1.1) with the observed vector y 2 R N , a closed parameter space \Theta ` R m , m ! N , int(\Theta) 6= ;. We suppose that the mapping j(\Delta) is one-to-one and continuous on \Theta, has continuous second order derivatives on int(\Theta), and that the matrix J(#) : = r T # j(#) has a full rank for every # 2 int...