A Bayesian uncertainty quantification analysis of $\alpha$-decay half-life calculations using both the distorted wave Born approximation (DWBA) and Wentzel-Kramers-Brillouin (WKB) methods has been involved in this work. Taking $N=127$ isotones as the examples, I employ Markov chain Monte Carlo sampling to explore the posterior distributions of potential parameters and the spectroscopic factor. This analysis shed light on fundamental differences in the properties of models: DWBA exhibits stronger parameter correlations and multimodal posteriors, reflecting its sensitivity to quantum mechanical constraints, while WKB shows more stable unimodal distributions. Both models achieve comparable accuracy in reproducing experimental half-lives. However, DWBA yields systematically wider 95% credible intervals, providing more conservative uncertainty estimates that reflect the challenges of enforcing strict quantum conditions, whereas WKB produces tighter intervals due to its lower parameter sensitivity. The Bayesian framework thus offers quantitative criteria for model selection based on the degree of alignment between model complexity and the underlying physical scale. This work provides new insights into uncertainty quantification of $\alpha$-decay models and establishes a quantitative criterion based on the alignment between a model's effective degrees of freedom and the physical scale of the probed system. These findings offer practical guidance for future theoretical studies of superheavy nuclei.

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• Alpha decay
• Lifetimes & widths
• Nuclear structure & decays
• Bayesian methods
• Optical, coupled-channel & distorted wave models