Mixture prior with a Dirac delta function and a normal distribution

General
1

Hi,

I would like to define a prior dictribution, which is a mixture of a dirac delta function with mass at 0 and a normal distribution. And I wonder if I could possibly code that in Stan. I feel like for location 0 it’s a discrete point, so might not be easy to implement.

Thank you for your suggestions on this!

2

It’s possible, but not at all recommended; spike & slab priors like this one don’t work well in Stan. A better alternative that can accomplish the same general goal is a regularized horseshoe prior (the link describes how to use it in brms, but you can also search for more info on this board).

3

Thanks so much for your kindly reply! I would check the reference for the regulairzed horseshoe prior. However, I am also very interested in how could we implement the mixture prior of a dirac delta function with mass at 0 and a normal distribution in Stan. Could you provide me some sample code on it?

Thanks!