Accurately estimating correlations between demographic parameters: A comment on Deane et al. (2023)

Area of Science:

• Population Ecology
• Quantitative Ecology
• Statistical Modeling

Background:

• Estimating correlations among demographic parameters is crucial in population ecology.
• A recent study by Deane et al. (2023) investigated the impact of covariance matrix priors on mark-recovery data inference.
• However, Deane et al. (2023) incorrectly parameterized their models, leading to flawed conclusions.

Purpose of the Study:

• To identify and correct a critical modeling error in Deane et al. (2023).
• To demonstrate an appropriate statistical method for analyzing covariance matrix priors in mark-recovery studies.
• To re-evaluate the influence of different priors on demographic parameter inference.

Main Methods:

• Detailed description of the parameterization error in Deane et al. (2023).
• Implementation of an alternative, statistically sound modeling approach.
• Comparative analysis of inference under different prior specifications (informative vs. vague) for covariance matrices.

Main Results:

• The original study by Deane et al. (2023) examined the effects of incorrect equations, not different priors.
• Our corrected analysis shows that informative inverse Wishart priors can indeed lead to flawed inference.
• Vague priors on covariance matrix components have minimal impact on inference when sample sizes are adequate.

Conclusions:

• The choice of priors and model parameterization significantly impacts demographic inference in population ecology.
• Informative priors, particularly inverse Wishart, should be used with caution due to their potential to bias results.
• Vague priors offer a more robust approach, especially with sufficient sample sizes, ensuring reliable population parameter estimates.