# Turing's summary statistics - ESS

**URL:** <https://discourse.julialang.org/t/turings-summary-statistics-ess/103537>\
**Category:** Statistics\
**Tags:** question, turing\
**Created:** [September 5, 2023, 9:18am UTC](https://discourse.julialang.org/t/turings-summary-statistics-ess/103537 "2023-09-05T09:18:12Z")\
**Posts on this page:** 1\
**Showing post:** 2

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**Author:** ![skleinbo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/skleinbo/32/36080_2.png) [@skleinbo](https://discourse.julialang.org/u/skleinbo)\
**Post date:** [September 8, 2023, 10:16am UTC](https://discourse.julialang.org/t/turings-summary-statistics-ess/103537/2 "2023-09-08T10:16:26Z")

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The documentation of `MCMCChains.rhat` references the paper [https://arxiv.org/pdf/1903.08008.pdf](https://arxiv.org/pdf/1903.08008.pdf)  
from which it apparently takes the calculation of `rhat` (and `ess`?).  
I have only skimmed over the first two pages just now, and hope I do understand correctly. The authors make the point that in general the convergence of MCMC cannot be reliably assessed from a single chain.

Thus, those observables are not calculated for every chain separately, which explains the identical values you observe. You may force a split by calling `ess_rhat(chains[:,:,1])` etc., but again, those might not reliably report failed convergence and overestimate the ESS.

(_P.S.: Please do not double post ['ESS' in Turing.jl](https://discourse.julialang.org/t/ess-in-turing-jl/103650) if a question doesn’t receive any attention for a couple of days. That happens. Instead, you can bump it with a comment after a while._)

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