Abstract Regression models are widely used statistical procedures, and the validation of their assumptions plays a crucial role in the data analysis process. Unfortunately, validating assumptions usually depends on the availability of tests tailored to the specific model of interest. A novel Bayesian goodness-of-fit hypothesis testing approach is presented for a broad class of regression models the response variable of which is univariate and continuous. The proposed approach relies on a suitable transformation of the response variable and a Bayesian prior induced by a predictor-dependent mixture model. Hypothesis testing is performed via Bayes factor, the asymptotic properties of which are discussed. The method is implemented by means of a Markov chain Monte Carlo algorithm, and its performance is illustrated using simulated and real data sets.

中文翻译：

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用于回归的贝叶斯拟合优度检验

摘要 回归模型是广泛使用的统计程序，其假设的验证在数据分析过程中起着至关重要的作用。不幸的是，验证假设通常取决于针对特定感兴趣模型的测试的可用性。提出了一种新的贝叶斯拟合优度假设检验方法，用于响应变量是单变量和连续的一大类回归模型。所提出的方法依赖于响应变量的适当变换和由依赖于预测变量的混合模型诱导的贝叶斯先验。假设检验是通过贝叶斯因子进行的，讨论了其渐近特性。该方法是通过马尔可夫链蒙特卡罗算法实现的，并使用模拟和真实数据集说明了其性能。