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How do Bayesian's treat the Bias Variance Tradeoff?

Typically the Bias Variance Tradeoff is expressed as $Bias^2 + Variance + irreducible\_error$, however wouldn't choosing a prior introduce bias and therefore decrease variance? And don't Bayesians not believe in irreducible error, only error that hasn't been explained yet? How do Bayesians perceive this Bias-Variance Tradeoff when they model and balance bias/variance for making predictions?

Also... do Bayesian cross-validate? How would they estimate a real-world test error?

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  • $\begingroup$ The last line is a different question, making your post too broad. I suggeest you split it up into two. $\endgroup$ Mar 6, 2020 at 18:59

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