# Potential Scale Reduction and chains=1

**URL:** <https://discourse.mc-stan.org/t/potential-scale-reduction-and-chains-1/2281>\
**Category:** General\
**Created:** [October 23, 2017, 3:10pm UTC](https://discourse.mc-stan.org/t/potential-scale-reduction-and-chains-1/2281 "2017-10-23T15:10:21Z")\
**Posts on this page:** 8\
**Page:** 1

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**Author:** ![Marcelo\_Silva](https://avatars.discourse-cdn.com/v4/letter/m/a3d4f5/32.png) [@Marcelo\_Silva](https://discourse.mc-stan.org/u/Marcelo_Silva)\
**Post date:** [October 23, 2017, 3:10pm UTC](https://discourse.mc-stan.org/t/potential-scale-reduction-and-chains-1/2281/1 "2017-10-23T15:10:21Z")

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Hi, would anyone know how Stan calculates the Rhat value using only one chain?

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**Author:** ![jkbest2](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jkbest2/32/4260_2.png) [@jkbest2](https://discourse.mc-stan.org/u/jkbest2)\
**Post date:** [October 23, 2017, 4:03pm UTC](https://discourse.mc-stan.org/t/potential-scale-reduction-and-chains-1/2281/2 "2017-10-23T16:03:35Z")

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I remember reading somewhere that for effective sample size calculations a single chain will be split in half. It’s probably the same for R hat.

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**Author:** ![bgoodri](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/bgoodri/32/4451_2.png) [@bgoodri](https://discourse.mc-stan.org/u/bgoodri)\
**Post date:** [October 23, 2017, 4:10pm UTC](https://discourse.mc-stan.org/t/potential-scale-reduction-and-chains-1/2281/3 "2017-10-23T16:10:03Z")

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Perhaps you are remembering from the Stan User Manual in the section entitled “Initialization and Convergence Monitoring”.

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**Author:** ![Marcelo\_Silva](https://avatars.discourse-cdn.com/v4/letter/m/a3d4f5/32.png) [@Marcelo\_Silva](https://discourse.mc-stan.org/u/Marcelo_Silva)\
**Post date:** [October 23, 2017, 5:02pm UTC](https://discourse.mc-stan.org/t/potential-scale-reduction-and-chains-1/2281/4 "2017-10-23T17:02:28Z")

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Wow! This is news to me. Thank you very much. I found something about this on page 479 of the Stan version 2.12.0 manual.

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**Author:** ![Marcelo\_Silva](https://avatars.discourse-cdn.com/v4/letter/m/a3d4f5/32.png) [@Marcelo\_Silva](https://discourse.mc-stan.org/u/Marcelo_Silva)\
**Post date:** [October 23, 2017, 5:04pm UTC](https://discourse.mc-stan.org/t/potential-scale-reduction-and-chains-1/2281/5 "2017-10-23T17:04:02Z")

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However, a reference about the subject would be interesting.

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**Author:** ![bgoodri](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/bgoodri/32/4451_2.png) [@bgoodri](https://discourse.mc-stan.org/u/bgoodri)\
**Post date:** [October 23, 2017, 6:23pm UTC](https://discourse.mc-stan.org/t/potential-scale-reduction-and-chains-1/2281/6 "2017-10-23T18:23:37Z")

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Don’t use Stan version 2.12.0 because the sampler was (slightly) broken, although the theory of split R-hat does not change in later versions. I think the only published explanation of it is in the BDA3 textbook, but Andrew might be working on a paper about it.

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**Author:** ![Bob\_Carpenter](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/bob_carpenter/32/9230_2.png) [@Bob\_Carpenter](https://discourse.mc-stan.org/u/Bob_Carpenter)\
**Post date:** [November 2, 2017, 9:22pm UTC](https://discourse.mc-stan.org/t/potential-scale-reduction-and-chains-1/2281/7 "2017-11-02T21:22:15Z")

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> [@Marcelo\_Silva](#):
>
> a reference about the subject would be interesting.

It’s in Gelman et al.'s _Bayesian Data Analysis_. And Andrew’s trying to put together a paper on split R-hat and ESS calculations that discount for non-convergence.

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**Author:** ![Marcelo\_Silva](https://avatars.discourse-cdn.com/v4/letter/m/a3d4f5/32.png) [@Marcelo\_Silva](https://discourse.mc-stan.org/u/Marcelo_Silva)\
**Post date:** [November 6, 2017, 1:27pm UTC](https://discourse.mc-stan.org/t/potential-scale-reduction-and-chains-1/2281/8 "2017-11-06T13:27:39Z")

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Thank you, prof. Carpenter.