{poscosea} : A Computationally Efficient Sensitivity Analysis for Bayesian Models using the posterior covariance representation

Abstract: Bayesian methods are essential in modern data analysis in ecology and evolutionary biology. They provide a flexible framework for modeling complex data-generating processes, while quantifying uncertainty based on the classical subjective interpretation of probability. However, Bayesian inference may provide misleading measures of uncertainty, particularly when the fitted model fails to adequately represent the true data-generating process. Although nonparametric approaches such as leave-k-out diagnostics and bootstrap resampling offer more robust alternatives under model misspecification, their computational cost is often too demanding because they require repeatedly refitting the same Bayesian model. In this paper, we introduce posterior covariance sensitivity analysis (PosCoSeA), a computationally efficient strategy for approximating leave-k-out diagnostics and bootstrap resampling without repeated model refitting. The performance of the methods is evaluated through both simulation studies and an application to real ecological data. We also provide an \textsf{R} package that implements these methods to facilitate their practical application.