I am performing linear regression with no intercept where I know that many of the independent variables are not relevant. I have given the coefficients of my regression regularized horseshoe prior distributions (https://arxiv.org/abs/1707.01694 (eqn. 2.8)). I have essentially copied the model from appendix C.1. However, since the independent variables have very different variances then those with higher variances are being treated as more relevant. What is the correct way to adjust the scales of the local parameters so that I donâ€™t have to scale my independent variables to have unit variance?

If I have not provided enough information or my question is vague please let me know and I will clarify. Thanks in advance.