A0521
Title: Bayesian ridge regression for survival data based on a vine copula based prior
Authors: Takeshi Emura - The Institute of Statistical Mathematics (Japan) [presenting]
Hirofumi Michimae - Kitasato University (Japan)
Abstract: 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. 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 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. It is also shown 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.
