I set my parameter to gamma[s][d] ~ normal(0, 0.01); but still see numbers like 4.60185. why would HMC take it so far out from the mean?
HMC is just fitting your posterior. 460 standard deviations is extreme. What does the rest of the data look like using that gamma? Remember, it’s not just the prior, but also the likelihood and all the other parameters that will affect a parameter’s marginal posterior.
Did the model converge to R-hat near 1 and reasonable effective sample size with multiple diffuse initializations? If so, it’s almost certainly an issue with model misspecification, not with HMC.