Quantify the contribution of MCMC error to posterior-covariance approximation variability

Investigate the contribution of MCMC error to the variability observed between exact leave-one-out refitting and posterior-covariance approximations for N-mixture models, particularly for the abundance-intercept parameter and total abundance.

Background

The paper evaluates posterior-covariance leave-one-out approximations for N-mixture models and compares them with estimates obtained by repeatedly refitting the model. The agreement is weaker for some inferential targets than in the generalized linear mixed-model example. The authors attribute part of this variability to the greater Monte Carlo error associated with the Metropolis-based sampling scheme used for the N-mixture model and note that increasing the number of MCMC iterations might improve agreement. However, the extent to which MCMC error accounts for the observed discrepancies has not been determined.

References

Increasing the number of MCMC iterations could therefore improve the agreement between the exact refitting and the approximation, although the contribution of MCMC error to the observed variability remains to be investigated.

— {poscosea} : A Computationally Efficient Sensitivity Analysis for Bayesian Models using the posterior covariance representation  (2608.25426 - Ohkubo et al., 26 Aug 2026) in Section 4, Application to the N-mixture Model, discussion of Figure 2