R-squared for Bayesian regression models

Andrew Gelman, Ben Goodrich, Jonah Gabry, Aki Vehtari

Research output: Contribution to journalArticleScientificpeer-review

73 Citations (Scopus)
249 Downloads (Pure)


The usual definition of R 2 (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.
Original languageEnglish
Pages (from-to)1-6
Number of pages6
Publication statusPublished - 1 Jan 2019
MoE publication typeA1 Journal article-refereed


  • Bayesian methods
  • R-squared
  • Regression

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