thank you very much for your thoughts! I am glad that you had time to read our paper, and even write almost a review about it. I would like to add three comments:

Firstly, our remark about the improper prior on g is indeed not well formulated. Although in our paper we cannot use an improper prior on g because the intercept is not comprised in the g-prior, you actually can use an improper prior on g if you treat the intercept like the other regression coefficients, as you do in “Bayesian Core”. However, we do not want to penalise the size of the intercept so we treat it separate and assign it a flat prior. Of course, including it in the g-prior may also have advantages.

Secondly, since the prior on g is treated generally in the paper (only the density f(g) is used), we are not restricted to the use of Cui and George’s incomplete inverse-gamma prior. The latter is only included for illustration of the performance of the computational strategy in the conjugate normal case.

Thirdly, the MCMC computations are indeed based on a linear interpolation of (Laplace approximated) posterior z=log(g) ordinates to get a proposal density for z (this is the dashed line in Figure 2). We also tried some spline interpolations here, but they were unstable and did not yield higher acceptance rates.

Best regards,

Daniel

P.S.: We are also glad that you enjoyed the literature review, and we would be happy if you cite the paper in “Bayesian Core”!

]]>