Ridge regression estimators can be interpreted as a Bayesian posterior mean (or mode) when the regression coefficients follow multivariate normal prior. However, the multivariate normal prior may not give efficient posterior estimates for regression coefficients, especially in the presence of interaction terms. In this paper, the vine copula-based priors are proposed for Bayesian ridge estimators under the Cox proportional hazards model. The semiparametric Cox models are built on the posterior density under two likelihoods: Cox’s partial likelihood and the full likelihood under the gamma process prior. The simulations show that the full likelihood is generally more efficient and stable for estimating regression coefficients than the partial likelihood. We also show via simulations and a data example that the Archimedean copula priors (the Clayton and Gumbel copula) are superior to the multivariate normal prior and the Gaussian copula prior.

当回归系数遵循多变量正态先验时，岭回归估计量可以解释为贝叶斯后验均值（或模式）。然而，多变量正态先验可能无法为回归系数提供有效的后验估计，尤其是在存在交互项的情况下。在本文中，针对 Cox 比例风险模型下的贝叶斯岭估计量，提出了基于 vine copula 的先验。半参数 Cox 模型建立在两种似然下的后验密度上：Cox 的部分似然和先验伽马过程下的完全似然。模拟表明，对于估计回归系数，完全似然通常比部分似然更有效和稳定。