Efficient approximation of post-processing posterior predictive p value with economic applications

Abstract

This paper addresses the computational challenges of calculating post-processing posterior predictive p-values by introducing a novel approximation method using the asymptotic pivotal discrepancy function. Existing approaches usually have a heavy computational burden due to the adoption of resampling in calculation. Our study proposes an efficient alternative by employing a posterior-based Wald-type discrepancy function, which can eliminate the need for resampling and significantly reduce computational demands. Through simulations, we demonstrate that our method achieves comparable results to computationally intensive approaches while offering substantial computational efficiency gains. We further validate our approach using two real-world datasets: CEO compensation and firm performance (analyzed via linear regression) and daily Pound/Dollar exchange rates (modeled using stochastic volatility). Our findings highlight the method’s adaptability and efficacy across diverse applications, advancing the practicality of Bayesian model evaluation and inference.