Smoothness Priors and Nonlinear Regression

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Abstract
Smoothness priors represent prior information that an unknown function does not change slope quickly and hence that the function describes a simple curve (e.g., Wahba 1978). In this article such priors for the multiple nonlinear regression model are developed in such a way that estimates and “standard errors” can be obtained as a natural and conceptually straightforward extension of linear multiple-regression estimation with the addition of dummy variables and dummy observations. Relations to spline and polynomial interpolation are described. An illustrative example of cost-function estimation is provided.

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