I've been working on Griddy Gibbs sampler (paper: Ritter and Tanner) and I've implemented it in R. But I've faced a problem when I started thinking on its uses in other contexts.
If I try to use an impoper uniform prior in a non conjugate setting, I'm supposed to perform numerical integration with the lower and upper bounds of the priors.
When using flat priors for continuous values, the upper and lower values are simply minus and plus infinity. Thus, it is not possible to have a grid approximation to this interval.
Are there any methods to handle this configuration? So far, I've been happy with the results of my sampler, but this feels like a situation that I can't handle with my current method.