ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 61, 2 (1992)
pp. 263-276

GEOMETRY OF THE NONLINEAR REGRESSION WITH PRIOR
A. PAZMAN

Abstract. In a nonlinear regression model with a given prior distribution, the estimator maximizing the posterior proba% bility density is considered (a certain kind of Bayes estimator). It is shown that the prior influences essential% ly, 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.

AMS subject classification. 62J02; Secondary 62F15, 62F11
Keywords. nonlinear regression, Bayes estimator, distribu% tions of estimators, geometry in statistics, curvatures

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Acta Mathematica Universitatis Comenianae
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Comenius University
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