Abstract:
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In the context of semi-parametric regression with multiple covariates, it is known that the solution to the penalized least squares minimization problem can be interpreted as the mean of a Gaussian process arising from the posterior distribution of an empirical Bayesian approach. Using the Representer Theorem, we propose a Bayesian regression model with normal distributed errors at the response level and prove that conditionally to the variance, it defines the same Gaussian Process. A Gaussian process which approximates the solution to the penalized least squares minimization problem using its mean function is described. We study using simulations, the performance of the means of the posterior predictive as point estimates for the regression function and the empirical coverage of the pointwise credible intervals from the the posterior predictive distributions of the approximated Gaussian Process.
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