GSF & SF Models have excessively confident credible intervals

[gowerc]

Re-running the GSF and SF models multiple times it appears that the value of sigma iterates around the true value as expected however the credible intervals are way too narrow and often miss the true value. So far have been unable to determine what causes this.

For example:

# A tibble: 8 × 7
  variable               mean    q01    q99  rhat ess_bulk ess_tail
  <chr>                 <dbl>  <dbl>  <dbl> <dbl>    <dbl>    <dbl>
1 lm_gsf_sigma         0.0134 0.0131 0.0138  1.00    5659.    3532.
2 lm_gsf_omega_bsld[1] 0.203  0.185  0.223   1.00   13736.    2929.
3 lm_gsf_omega_kg[1]   0.218  0.190  0.250   1.00    5547.    3216.
4 lm_gsf_omega_kg[2]   0.193  0.167  0.222   1.00    5664.    3449.
5 lm_gsf_omega_ks[1]   0.310  0.265  0.359   1.00    6288.    4103.
6 lm_gsf_omega_ks[2]   0.306  0.260  0.357   1.00    6819.    3813.
7 lm_gsf_omega_phi[1]  0.0946 0.0539 0.144   1.02     287.     461.
8 lm_gsf_omega_phi[2]  0.102  0.0617 0.153   1.01     261.     486.

Note that all other values appear to be accurate and as expected so not sure what is going wrong here.