Model averaging is commonly used to allow for model uncertainty in parameter estimation. As well as providing a point estimate that is a natural compromise between the estimates from different models, it also provides confidence intervals with better coverage properties, compared to those based on a single best model. In recent years, the concept of a confidence distribution has been promoted as a frequentist analogue of a Bayesian posterior distribution. The confidence distribution for a parameter is a visual representation of the set of \(100(1-\alpha )\%\) confidence intervals for all possible \(\alpha \), and was first proposed over 60 years ago. The purpose of this paper is to promote the use of model-averaged confidence distributions. One of the advantages of doing so is the ability to see unusual shapes in the distribution, such as multi-modality. This allows a more comprehensive assessment of the uncertainty about the parameter of interest, in exactly the same way that a model-averaged posterior distribution can be more useful than a model-averaged credible interval. We show that the model-averaged tail-area (MATA) method for calculating a model-averaged confidence interval leads to the corresponding MATA confidence distribution being a mixture of the confidence distributions associated with the individual models, the mixing being determined by the model weights. We consider two ecological examples that illustrate the advantages of a model-averaged confidence distribution over a model-averaged confidence interval.

中文翻译：

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模型平均置信度分布

模型平均通常用于在参数估计中考虑模型不确定性。与基于单个最佳模型的那些点相比，除了提供一个点估计值（这是不同模型的估计值之间的自然折衷）之外，它还提供了具有更好覆盖范围的置信区间。近年来，置信度分布的概念已被推广为贝叶斯后验分布的常识类似物。参数的置信度分布是所有可能\（\ alpha \）的\（100（1- \ alpha）\％\）置信区间集合的直观表示，最早是在60多年前提出的。本文的目的是促进模型平均置信度分布的使用。这样做的优点之一是能够看到分布中的异常形状，例如多模式。这样就可以更全面地评估感兴趣参数的不确定性，完全相同，模型平均后验分布比模型平均可信区间更有用。我们表明，用于计算模型平均置信区间的模型平均尾部面积（MATA）方法导致对应的MATA置信分布是与各个模型相关联的置信分布的混合，混合由模型权重确定。