In health sciences, identifying the leading causes that govern the behaviour of a response variable is a question of crucial interest. Formally, this can be formulated as a variable selection problem. In this paper, we introduce the basic concepts of the Bayesian approach for variable selection based on model choice, emphasizing the model space prior adoption and the algorithms for sampling from the model space and for posterior probabilities approximation; and show its application to two common problems in health sciences. The first concerns a problem in the field of genetics while the second is a longitudinal study in cardiology. In the context of these applications, considerations about control for multiplicity via the prior distribution over the model space, linear models in which the number of covariates exceed the sample size, variable selection with censored data, and computational aspects are discussed. The applications presented here also have an intrinsic statistical interest as the proposed models go beyond the standard general linear model. We believe this work will broaden the access of practitioners to Bayesian methods for variable selection.

中文翻译：

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贝叶斯变量选择及其在健康科学中的应用

在卫生科学中，确定控制响应变量行为的主要原因是至关重要的问题。形式上，这可以表述为变量选择问题。在本文中，我们介绍了基于模型选择的贝叶斯方法进行变量选择的基本概念，强调了模型空间的先验采用以及从模型空间进行采样和后验概率近似的算法；并将其应用于健康科学中的两个常见问题。第一个涉及遗传学领域的问题，第二个涉及心脏病学的纵向研究。在这些应用的背景下，需要考虑通过模型空间中先验分布控制多重性，协变量数量超过样本大小的线性模型，讨论了带有审查数据的变量选择以及计算方面。由于提出的模型超出了标准的一般线性模型，因此此处介绍的应用程序也具有内在的统计兴趣。我们相信这项工作将拓宽从业者使用贝叶斯方法进行变量选择的范围。