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bob-carpenter
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bob-carpenter
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Thanks, Abner. This is a great start.
As I suggested during the Stan meeting, it's very challenging to express math and stats simply in a way that's not wrong. I listed a whole bunch of changes I think are necessary in this regard. I'm happy to hop on a call or discuss more during the Stan meeting.
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| - part: "Usage" | ||
| chapters: | ||
| - glossary.qmd |
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I think the glossary should be last in the list here.
| unfamiliar with Stan's vocabulary. | ||
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| The explanations included here are not intended to be exhaustive or detailed. | ||
| For more information, consult our chapter [*How to Diagnose and Resolve |
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Please keep to third person and remove the "our".
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| **Bulk ESS** A version of the effective sample size that measures the | ||
| reliability of the center, or "bulk", of the posterior distribution, i.e., the | ||
| region summarized by a mean or a median. A high bulk ESS indicates that |
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Which is it, mean or median? I've never quite understood this concept myself, so I'm not sure. But with many distributions medians and means can be pretty far apart with enough skew.
| reliability of the center, or "bulk", of the posterior distribution, i.e., the | ||
| region summarized by a mean or a median. A high bulk ESS indicates that | ||
| estimates of the distribution's central tendency are reliable. See also: | ||
| *Effective sample size*, *Tail ESS*. |
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It would be better if these were links.
| estimates of the distribution's central tendency are reliable. See also: | ||
| *Effective sample size*, *Tail ESS*. | ||
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| **Chain** An ordered sequence of random draws produced by a sampler to |
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I think this should say that it's a Markov chain, but then that's not true during warmup.
| intended for reporting. So, if we plan to report two decimal places, the MCSE | ||
| should be below $0.01$. See also: *Effective sample size*, *Iteration*. | ||
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| **R-hat** A diagnostic that evaluates whether multiple chains have converged |
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diagnostic -> statistic of multiple chains
It doesn't evaluate, it tests. And it's not a foolproof test in that there are false positives and false negatives.
The two types of variation do not become equal. Rhat is essential sqrt(1 + between/within). The idea is that the between variation goes to 0 and the within stays constant at its nominal value based on the model, so that Rhat converges to 1.
Charles Margossian's nested R-hat paper is super useful for understanding what R-hat is doing.
| within each chain to the variation across different chains. When chains | ||
| converge, these two types of variation become roughly equal, so R-hat gets | ||
| close to 1. When chains diverge, the variation across different chains is | ||
| larger than the variation within chains, so R-hat is above 1. See a formal |
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What's happening is that the within chain variation scales the between chain variation to make R-hat unit free.
| thresholds [here](https://mc-stan.org/learn-stan/diagnostics-warnings.html#r-hat). | ||
| See also: *Chain*. | ||
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| **Reparametrize** To rewrite a model in a different but mathematically |
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They're not mathematically equivalent in that they define two different densities (otherwise there wouldn't be much point). The idea is that the posteriors have enough information to derive each others random variables of interest.
Stan can always represent a model in infinitely many different ways.
Centering a predictor does not leave the model the same---it shifts things from coefficients into the intercept in a regression, for example. The point is that the centered posterior draws can be transformed to non-centered posterior draws.
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| **Tail ESS** A version of the effective sample size that measures the | ||
| reliability of the tails of the posterior distribution, i.e., the regions | ||
| summarized by the 5% or 95% posterior quantiles. A high tail ESS indicates |
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Is this really the 5% and 95% quantiles? I don't know.
| that these quantiles are reliable. See also: *Bulk ESS*, | ||
| *Effective sample size*. | ||
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| **Warmup** An initial set of iterations that are discarded rather than used |
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You're describing what people call "burn in" despite Gelman's objections that it's a bad analogy. In Stan, warmup critically does adaptation. As such, it doesn't form a Markov chain. We just assume that the adaptation will also take care of burn in.
There are three warmup phases. Phase I attempts to burn in with a unit mass matrix. Phase II attempts to estimate the mass matrix. Phase III does a final tuning of step size.
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<<{ since VERSION }>>Summary
Add a glossary of technical terms used in Stan interfaces.
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Please list the copyright holder for the work you are submitting (this will be you or your assignee, such as a university or company): Abner Heredia Bustos
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