The following is a list of errors in the published and peer-reviewed article:

Everink, J. M., Dong, Y., & Andersen, M. S. (2023). Bayesian inference with projected densities. SIAM/ASA Journal on Uncertainty Quantification, 11(3), 1025-1043.

Errors mentioned in appendix PhD thesis:

• Lemma 2.3: Some of the equalities should be proportional, due to a missing constant Jacobian in the proof. In particular:
  • The second equation in Lemma 2.3. should read: \(\pi_F(z)\,\propto\, \int_{\Sigma N_C} \pi_{x^\star}(z + v)\text{d}v.\)
  • The equation in the proof should read: \(\mathbb{P}(\Pi_C^{\Sigma^{-1}}(x^\star) \in E)\,=\, \int_{E + \Sigma N_C}\pi_{x^\star}(w)\text{d}w \propto \pi_F(z)\,\propto\, \int_{\Sigma N_C}\int_{E} \pi_{x^\star}(z + v)\text{d}v\text{d}z.\)
• Figure 7: In the top two subplots regarding the Autocorrelation Function (ACF) for \(\lambda\) and \(\delta\), the data labels are incorrect. Whilst the conclusions do not change, the correct data shown is the following:
  • ACF for \(\lambda\), unconstrained is the only correct one.
  • ACF for \(\lambda\), with nonnegativity shows ACF for \(\delta\), with nonnegativity.
  • ACF for \(\delta\), unconstrained shows ACF for \(\lambda\), with nonnegativity.
  • ACF for \(\delta\), with nonnegativity shows ACF for \(\delta\), unconstrained.