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Stan is software for Bayesian estimation using the No-U-Turn sampling (NUTS) algorithm instead of the simpler Gibbs sampling (BUGS).

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What is the difference between hierarchical modeling and setting a (fixed) prior on a parame...

If I were to fit this model in Stan, I would specify a prior on $\beta_0, \beta_1, \sigma^2$, and $\sigma^2_\alpha$. …
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