“R-squared for Bayesian Regression Models” (2018), by Andrew Gelman et al. Mathematics research paper. Original abstract below, unchanged. No free PDF was found.

R-squared for Bayesian Regression Models

Andrew Gelman, Ben Goodrich, Jonah Gabry et al. · December 10, 2018 · Mathematics

Abstract

The usual definition of R2 (variance of the predicted values divided by the variance of the data) has a problem for Bayesian fits, as the numerator can be larger than the denominator. We propose an alternative definition similar to one that has appeared in the survival analysis literature: the variance of the predicted values divided by the variance of predicted values plus the expected variance of the errors.

Source page DOI: 10.1080/00031305.2018.1549100