Data analyses typically rely upon assumptions about the missingness mechanisms that lead to observed versus missing data, assumptions that are typically unassessable. We explore an approach where the joint distribution of observed data and missing data are specified in a nonstandard way. In this formulation, which traces back to a representation of the joint distribution of the data and missingness mechanism, apparently first proposed by J. W. Tukey, the modeling assumptions about the distributions are either assessable or are designed to allow relatively easy incorporation of substantive knowledge about the problem at hand, thereby offering a possibly realistic portrayal of the data, both observed and missing. We develop Tukey’s representation for exponential-family models, propose a computationally tractable approach to inference in this class of models, and offer some general theoretical comments. We then illustrate the utility of this approach with an example in systems biology.

数据分析通常依赖于关于导致观察到的数据丢失的缺失机制的假设，这些假设通常是无法评估的。我们探索了一种以非标准方式指定观察数据和缺失数据的联合分布的方法。在这种表述可以追溯到数据和缺失机制的联合分布的表示形式（显然是由JW Tukey首先提出的）中，有关分布的建模假设可以评估或设计为允许相对容易地并入有关该分布的实质性知识。眼前的问题，从而可能对观察到的和丢失的数据进行现实的描绘。我们为指数族模型开发了Tukey的表示形式，在此类模型中提出了一种计算上容易处理的方法，并提供了一些一般性的理论评论。然后，我们以系统生物学为例来说明这种方法的实用性。