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A1090
Title: The R2D2 prior for generalized linear mixed models Authors:  Eric Yanchenko - North Carolina State University / Tokyo Institute of Technology (Japan) [presenting]
Abstract: In Bayesian analysis, the selection of a prior distribution is typically done by considering each parameter in the model. While this can be convenient, it may be desirable to place a prior on a summary measure of the model instead of in many scenarios. A prior on the model fit is proposed, as measured by a Bayesian coefficient of determination ($R^2$), which then induces a prior on the individual parameters. This is achieved by placing a beta prior on $R^2$ and then deriving the induced prior on the global variance parameter for generalized linear mixed models. Closed-form expressions are derived 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, approximating the prior is suggested by using a generalized beta prime distribution and a simple default prior construction scheme is provided. This approach is quite flexible and can be easily implemented in standard Bayesian software. Lastly, the method's performance is demonstrated on simulated data, where it particularly shines in high-dimensional examples and real-world data, which shows its ability to model spatial correlation in the random effects.