The multi-modal posterior under unidentified nonparametric models yields poor mixing of Markov Chain Monte Carlo (MCMC), which is a stumbling block to Bayesian predictions. In this article, we conceptualize a prior informativeness threshold that is essentially the variance of posterior modes and expressed by the uncertainty hyperparameters of nonparametric priors. The threshold plays the role of a lower bound of the within-chain MCMC variance to ensure MCMC mixing, and engines prior modification through hyperparameter tuning to descend the mode variance. Our method distinguishes from existing postprocessing methods in that it directly samples well-mixed MCMC chains on the unconstrained space, and inherits the original posterior predictive distribution in predictive inference. Our method succeeds in Bayesian survival predictions under an unidentified nonparametric transformation model, guarded by the inferential theories of the posterior variance, under elicitation of two delicate nonparametric priors. Comprehensive simulations and real-world data analysis demonstrate that our method achieves MCMC mixing and outperforms existing approaches in survival predictions.

翻译：未识别非参数模型下的多峰后验分布会导致马尔可夫链蒙特卡洛（MCMC）混合效果不佳，这成为贝叶斯预测的主要障碍。本文提出了一个先验信息性阈值的概念，该阈值本质上是后验众数的方差，并通过非参数先验的不确定性超参数来表达。该阈值充当了链内MCMC方差的下界，以确保MCMC混合，并通过超参数调优来降低众数方差，从而驱动先验修正。我们的方法区别于现有的后处理方法，因为它直接在无约束空间上采样混合良好的MCMC链，并在预测推断中继承了原始的后验预测分布。在两种精细非参数先验的设定下，我们的方法在后验方差推断理论的保障下，成功应用于未识别非参数变换模型的贝叶斯生存预测。综合模拟和真实数据分析表明，我们的方法实现了MCMC混合，并在生存预测中优于现有方法。