For the JAGS/stan versions, I think if we have a known observation error in abundances (or can provide a prior on it), we could separate out variance due to observations and that due to underlying process variation. For JAGS, we would simply add another variance term in the model equation. For stan, I don't think we could use pre-compiled Rstanarm, so may have to compile our the code. This may improve the estimates of decline, not sure.
For the JAGS/stan versions, I think if we have a known observation error in abundances (or can provide a prior on it), we could separate out variance due to observations and that due to underlying process variation. For JAGS, we would simply add another variance term in the model equation. For stan, I don't think we could use pre-compiled Rstanarm, so may have to compile our the code. This may improve the estimates of decline, not sure.