Approximate Bayesian inference for the class of latent Gaussian models can be achieved efficiently with integrated nested Laplace approximations (INLA). Based on recent reformulations in the INLA methodology, we propose a further extension that is necessary in some cases like heavy-tailed likelihoods or binary regression with imbalanced data. This extension formulates a skewed version of the Laplace method such that some marginals are skewed and some are kept Gaussian while the dependence is maintained with the Gaussian copula from the Laplace method. Our approach is formulated to be scalable in model and data size, using a variational inferential framework enveloped in INLA. We illustrate the necessity and performance using simulated cases, as well as a case study of a rare disease where class imbalance is naturally present.

翻译：对于潜高斯模型类，可通过集成嵌套拉普拉斯近似（INLA）高效实现近似贝叶斯推断。基于INLA方法的最新重构，我们提出了一种在重尾似然或数据不平衡的二元回归等场景中必需的扩展方法。该扩展构建了拉普拉斯方法的偏态版本，使得部分边缘分布呈偏态而部分保持高斯分布，同时通过拉普拉斯方法的高斯Copula保持变量间的依赖关系。我们的方法采用包裹在INLA框架内的变分推断体系，确保其在模型与数据规模上具备可扩展性。我们通过模拟案例以及天然存在类别不平衡的罕见疾病案例研究，论证了该方法的必要性与性能表现。