In reading a book chapter on Bayesian Linear Regression, I came across a general statement by the author that:
"The value of the intercept ($\alpha$) is frequently uninterpretable without also studying any ($\beta$) parameters. This is why we need very weak priors for intercepts, in many cases".
I really am not clear what the author means as to the reason why the prior on $\alpha$ (the intercept), needs to be generally WIDER than the prior on $\beta$ (the slope)?
Could someone help me understand, in the context of a simple linear regression, that why we usually need to use a WIDER prior on on $\alpha$ (the intercept) compared to the prior on $\beta$ (the slope)?