论文标题
贝叶斯的预测与协变量受到检测极限
Bayesian Prediction with Covariates Subject to Detection Limits
论文作者
论文摘要
由于信号干扰或测量设备中缺乏敏感性而导致的协变量缺失值在工业问题中很常见。我们通过有效的马尔可夫链蒙特卡洛（MCMC）算法为预测问题提出了完整的贝叶斯解决方案，该算法在随机扫描吉布斯采样器中共同更新所有审查的协变量值。我们表明，与单变量更新相比，缺少协变量值的联合更新至少可以提高两个数量级。这种提高的效率被证明对于快速学习缺失的协变量值及其在实时决策环境中的不确定性至关重要，特别是当后部缺失值之间存在实质性相关性时。该方法对模拟数据和电信部门的数据进行评估。我们的结果表明，所提出的贝叶斯插补比幼稚的插补给出了更准确的预测，并且在插补中使用辅助变量可提供额外的预测能力。
Missing values in covariates due to censoring by signal interference or lack of sensitivity in the measuring devices are common in industrial problems. We propose a full Bayesian solution to the prediction problem with an efficient Markov Chain Monte Carlo (MCMC) algorithm that updates all the censored covariate values jointly in a random scan Gibbs sampler. We show that the joint updating of missing covariate values can be at least two orders of magnitude more efficient than univariate updating. This increased efficiency is shown to be crucial for quickly learning the missing covariate values and their uncertainty in a real-time decision making context, in particular when there is substantial correlation in the posterior for the missing values. The approach is evaluated on simulated data and on data from the telecom sector. Our results show that the proposed Bayesian imputation gives substantially more accurate predictions than naïve imputation, and that the use of auxiliary variables in the imputation gives additional predictive power.
