We discuss the role of misspecification and censoring on Bayesian model selection in the contexts of right-censored survival and concave log-likelihood regression. Misspecification includes wrongly assuming the censoring mechanism to be non-informative. Emphasis is placed on additive accelerated failure time, Cox proportional hazards and probit models. We offer a theoretical treatment that includes local and non-local priors, and a general non-linear effect decomposition to improve power-sparsity trade-offs. We discuss a fundamental question: what solution can one hope to obtain when (inevitably) models are misspecified, and how to interpret it? Asymptotically, covariates that do not have predictive power for neither the outcome nor (for survival data) censoring times, in the sense of reducing a likelihood-associated loss, are discarded. Misspecification and censoring have an asymptotically negligible effect on false positives, but their impact on power is exponential. We show that it can be advantageous to consider simple models that are computationally practical yet attain good power to detect potentially complex effects, including the use of finite-dimensional basis to detect truly non-parametric effects. We also discuss algorithms to capitalize on sufficient statistics and fast likelihood approximations for Gaussian-based survival and binary models.
翻译:我们讨论了在正确审查的生存和逻辑相似性回归的背景下,对巴伊西亚模式选择的错误区分和审查的作用。错误区分包括错误地假设审查机制是非信息规范的。强调的是累加加速故障时间、考克斯比例危害和线虫模型。我们提供了一种理论处理方法,包括地方和非地方前科,以及一般性的非线性影响分解,以改进权力平衡。我们讨论了一个根本问题:当(不可避免的)模型被错误地描述时,人们能够希望获得什么解决办法,以及如何加以解释? 误认为审查机制是非信息规范的。强调强调的是,从减少与可能性有关的损失的意义上讲,没有预测性加速故障时间,Cox比例危害和线性模型的偏差,以及一般的非线性影响,以改进权力平衡性权衡。我们指出,在(不可避免的)模型被误定义时,人们能够期望获得什么解决办法? 简单模型能够实现良好的能力,从而无法预测结果或(对于生存数据)审查时间,从减少与可能性相关的损失的意义上说,我们被抛弃了。区分和审查对错误模型的影响是微不足道的,但是它们对权力的影响是指数性的。我们指出,我们也可以考虑一些简单的模式是有利的。我们也可以考虑如何计算而获得良好的模型来检测到能够探测到充分的精确的精确的精确的精确的精确的逻辑基础,我们也用来探测到测量性统计基础。