I wrote a Stan program for a time-series model, and it works very nice, except that the time and response need to be rescaled/standardized before putting into the model. I use normal (0, 1) and cauchy (0,1) for priors.

I would prefer to obtain estimated parameters on original scale, while I found it algebraically challenging to recover the original parameters. So I am wondering whether I should choose wider prior distribution, for example, normal (0, 10) and cauchy (0, 5), to avoid the standardization of response variable? I tried this on a small example, and it seems working, but my another question is that if I encounter a new dataset with more extreme response values, do I have to change my prior distribution again in order to avoid standardization? In this case, is standardization a better option than to change prior distribution from time to time?

I am really new to Stan and Bayesian inference, hence what I asked might be naive and mistaken. But I would really appreciate if anyone can give me some suggestions. Thanks!