I want to construct a simple normal regression model. However, my prior information about beta0, beta1, and sigma is not in a closed analytical form (no specific distribution). Instead, I have 20,000 draws for each parameter. My aim is to get posterior draws for each parameter beta0, beta1, and sigma again. Is there a way to implement this in Stan? Or is this a case that MCMC algorithms cannot handle? (as far as I know, well-known MCMC algorithms require prior distribution of parameters). I do not want to lose information so I do not want to find an approximate distribution. I hope my question is clear.
Thanks in advance!