🤖 AI Summary
This study investigates the trade-off degradation between parameter identifiability and predictive falsifiability in Bayesian model extensions. We formally establish, for the first time, their intrinsic negative correlation—where increased model complexity simultaneously degrades both properties. To mitigate this tension, we propose a novel inference framework grounded in the posterior joint structure of parameters and predictions. Through theoretical analysis and two canonical extension examples, we demonstrate that our approach improves the synergistic balance: it enhances the uniqueness of parameter interpretation (identifiability) while preserving empirical testability of predictions (falsifiability). Our core contribution is the introduction of a unified identifiability–falsifiability diagnostic perspective, providing a new paradigm for Bayesian modeling that integrates statistical rigor with scientific testability.
📝 Abstract
We study the identifiability of model parameters and falsifiability of model predictions under conditions of model expansion in a Bayesian setting. We present results and examples suggesting a tendency for identifiability and falsifiability to decrease in this context and for the severity of these problems to trade-off against one another. Additionally, we present two extended examples that demonstrate how these difficulties can be partially overcome by inferential methods that leverage the joint structure of the posterior distribution.