In Bayesian analysis, the selection of a prior distribution is typically done by considering each parameter in the model. While this can be convenient, in many scenarios it may be desirable to place a prior on a summary measure of the model instead. In this work, we propose a prior on the model fit, as measured by a Bayesian coefficient of determination (R2), which then induces a prior on the individual parameters. We achieve this by placing a beta prior on R2 and then deriving the induced prior on the global variance parameter for generalized linear mixed models. We derive closed-form expressions in many scenarios and present several approximation strategies when an analytic form is not possible and/or to allow for easier computation. In these situations, we suggest to approximate the prior by using a generalized beta prime distribution that matches it closely. This approach is quite flexible and can be easily implemented in standard Bayesian software. Lastly, we demonstrate the performance of the method on simulated data where it particularly shines in high-dimensional examples as well as real-world data which shows its ability to model spatial correlation in the random effects.

翻译：在Bayesian分析中,选择先前的分布通常是通过考虑模型中的每个参数来完成的。 虽然这很方便, 但在许多假设中, 最好先先对模型进行简易测量。 在这项工作中, 我们建议先对模型是否合适进行事先测试, 以Bayesian确定系数(R2)进行测量, 然后再对单个参数进行检测。 我们这样做的方法是在R2上先放置一个贝塔, 然后再对通用线性混合模型的全球差异参数进行引证。 我们在许多假设中产生封闭式表达, 并在无法以分析形式进行分析和/ 或允许更方便地计算时提出几种近似战略。 在这些情况下, 我们建议通过使用与该模型密切匹配的通用的Bepin分布来对准之前的模型。 这种方法非常灵活, 可以在标准Bayesian软件中轻易实施。 最后, 我们演示模拟数据方法的性能, 模拟数据特别在高维度实例中闪亮, 以及真实世界数据显示其在随机效应中模拟空间相关性的能力。