A fast regression via SVD and marginalization

We describe a numerical scheme for evaluating the posterior moments of Bayesian linear regression models with partial pooling coefficients. The principal analytical tool evaluation is change basis from coefficient space to singular vectors matrix predictors. After this and an integration, we reduce problem finding density over $$k + 2$$ dimensions, 2-dimensional density, where k number Moments can then be computed using, example, MCMC, trapezoid rule, or adaptive Gaussian quadrature. An SVD predictors dominant computational cost performed once during precomputation stage. demonstrate results algorithm.