Multivariate Bayesian Regression Analysis Applied to Ground-Motion Prediction Equations, Part 1: Theory and Synthetic Example

An application of a linear multivariate Bayesian regression model to compute pseudoacceleration (SA) ground-motion prediction equations (GMPEs )i s presented. The model is able to include the correlation between observations for a given earthquake, the correlation between SA ordinates at different periods, and the correlation between regression coefficients of the ground-motion prediction model. We evaluate the advantages of the Bayesian approach over the traditional regression methods, and we discuss the differences between univariate and multivariate analyses. Because the application of the Bayesian method is in general complex and implies an increase in the numerical effort with respect to the traditional methods, our computer code to perform linear Bayesian analyses is freely available on request.

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