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A comment on Bayesian Data Analysis, Third edition [pdf]. Parent comment
Before Stan existed we used BUGS [1] and then JAGS [2]. And most of the work on computation (by Neal and others) was entirely independent of Gelman.
[1] https://en.wikipedia.org/wiki/Bayesian_inference_using_Gibbs...
[2] https://en.wikipedia.org/wiki/Just_another_Gibbs_sampler
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Before Stan existed we used BUGS [1] and then JAGS [2]. And most of the work on computation (by Neal and others) was entirely independent of Gelman.
[1] https://en.wikipedia.org/wiki/Bayesian_inference_using_Gibbs...
[2] https://en.wikipedia.org/wiki/Just_another_Gibbs_sampler