Bayesian inference correlation: From <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math>-particle preformation factor to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math>-decay p

In this study, we propose a novel Bayesian inference framework combined with the two-potential approach (TPA) to systematically investigate the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>α</a:mi></a:math>-particle preformation factors and decay properties of heavy and superheavy nuclei. By employing Markov chain Monte Carlo (MCMC) sampling, we globally calibrate the adjustable parameters of phenomenological <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>α</b:mi></b:math> preformation factors, while incorporating experimental uncertainties in decay energies and half-lives. Our results reveal a significant correlation between the parameters, and the nuclear shell effects near neutron magic numbers <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>N</c:mi><c:mo>=</c:mo><c:mn>126</c:mn></c:mrow></c:math>, 152, and 162 play a key role. The <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mn>95</d:mn><d:mo>%</d:mo></d:mrow></d:math> posterior confidence levels provided by the Bayesian method significantly enhance the reliability of parameter estimation, which is superior to traditional least-squares optimization. Notably, the derived preformation factors exhibit systematic deviations near shell closures, highlighting the necessity of explicitly incorporating nuclear structure effects. This work not only advances the precision of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>α</e:mi></e:math>-decay predictions but also offers a deeper understanding of shell evolution and collective effects in superheavy nuclei.