We propose a framework for fitting fractional polynomials models as special cases of Bayesian Generalized Nonlinear Models, applying an adapted version of the Genetically Modified Mode Jumping Markov Chain Monte Carlo algorithm. The universality of the Bayesian Generalized Nonlinear Models allows us to employ a Bayesian version of the fractional polynomials models in any supervised learning task, including regression, classification, and time-to-event data analysis. We show through a simulation study that our novel approach performs similarly to the classical frequentist fractional polynomials approach in terms of variable selection, identification of the true functional forms, and prediction ability, while providing, in contrast to its frequentist version, a coherent inference framework. Real data examples provide further evidence in favor of our approach and show its flexibility.

翻译：本文提出一个将分数多项式模型作为贝叶斯广义非线性模型特例进行拟合的框架，采用经过改进的遗传修饰模式跳跃马尔可夫链蒙特卡洛算法。贝叶斯广义非线性模型的普适性使我们能够在任何监督学习任务（包括回归、分类和事件时间数据分析）中应用分数多项式模型的贝叶斯版本。模拟研究表明，我们的新方法在变量选择、真实函数形式识别和预测能力方面与经典频率学派分数多项式方法表现相近，同时相比其频率学派版本提供了一致的推断框架。实际数据案例进一步支持了我们的方法并展示了其灵活性。