Elliptical slice sampling for Bayesian shrinkage regression with applications to causal inference
This paper specializes the elliptical slice sampler for Bayesian linear regression models with Gaussian errors and arbitrary shrinkage priors. The only requirement is that the shrinkage prior density function can be evaluated up to a normalizing constant. The new sampler draws all coefficients simultaneously and simulation studies show that it is markedly more efficient than the Gibbs samplers that are typically used for such models. It is demonstrated how to tailor the new sampling scheme to reparametrized linear regressions for causal inference treatment effect estimation and instrumental variables models.