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use https for mc-stan.org links in vignettes
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vignettes/graphical-ppcs.Rmd

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This vignette focuses on graphical posterior predictive checks (PPC). Plots of parameter estimates
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from MCMC draws are covered in the separate vignette
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[_Plotting MCMC draws_](http://mc-stan.org/bayesplot/articles/plotting-mcmc-draws.html),
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[_Plotting MCMC draws_](https://mc-stan.org/bayesplot/articles/plotting-mcmc-draws.html),
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and MCMC diagnostics are covered in the
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[_Visual MCMC diagnostics_](http://mc-stan.org/bayesplot/articles/visual-mcmc-diagnostics.html)
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[_Visual MCMC diagnostics_](https://mc-stan.org/bayesplot/articles/visual-mcmc-diagnostics.html)
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vignette.
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### Graphical posterior predictive checks (PPCs)
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To demonstrate some of the various PPCs that can be created with the
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**bayesplot** package we'll use an example of comparing Poisson and Negative
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binomial regression models from one of the
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**rstanarm** [package vignettes](http://mc-stan.org/rstanarm/articles/count.html)
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**rstanarm** [package vignettes](https://mc-stan.org/rstanarm/articles/count.html)
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(Gabry and Goodrich, 2017).
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> We want to make inferences about the efficacy of a certain pest management system at reducing the number of roaches in urban apartments. [...] The regression predictors for the model are the pre-treatment number of roaches `roach1`, the treatment indicator `treatment`, and a variable `senior` indicating whether the apartment is in a building restricted to elderly residents. Because the number of days for which the roach traps were used is not the same for all apartments in the sample, we include it as an exposure [...].
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There are many additional PPCs available, including plots of predictive
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intervals, distributions of predictive errors, and more. For links to the
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documentation for all of the various PPC plots see `help("PPC-overview")`
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from R or the [online documentation](http://mc-stan.org/bayesplot/reference/index.html#section-ppc) on the Stan website.
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from R or the [online documentation](https://mc-stan.org/bayesplot/reference/index.html#section-ppc) on the Stan website.
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The `available_ppc` function can also be used to list the names of all PPC
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plotting functions:
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Gabry, J., and Goodrich, B. (2017). rstanarm: Bayesian Applied Regression
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Modeling via Stan. R package version 2.15.3.
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http://mc-stan.org/rstanarm, https://CRAN.R-project.org/package=rstanarm
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https://mc-stan.org/rstanarm, https://CRAN.R-project.org/package=rstanarm
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Gabry, J. , Simpson, D. , Vehtari, A. , Betancourt, M. and Gelman, A. (2019),
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Visualization in Bayesian workflow. _J. R. Stat. Soc. A_, 182: 389-402.
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edition.
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Stan Development Team. (2017). *Stan Modeling Language Users
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Guide and Reference Manual*. http://mc-stan.org/users/documentation/
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Guide and Reference Manual*. https://mc-stan.org/users/documentation/

vignettes/plotting-mcmc-draws.Rmd

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This vignette focuses on plotting parameter estimates from MCMC draws. MCMC
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diagnostic plots are covered in the separate vignette
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[_Visual MCMC diagnostics_](http://mc-stan.org/bayesplot/articles/visual-mcmc-diagnostics.html),
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[_Visual MCMC diagnostics_](https://mc-stan.org/bayesplot/articles/visual-mcmc-diagnostics.html),
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and graphical posterior predictive model checking is covered in the vignette
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[_Graphical posterior predictive checks_](http://mc-stan.org/bayesplot/articles/graphical-ppcs.html).
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[_Graphical posterior predictive checks_](https://mc-stan.org/bayesplot/articles/graphical-ppcs.html).
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### Setup
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**rstanarm** package (Gabry and Goodrich, 2017), but MCMC draws from using
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any package can be used with the functions in the **bayesplot** package. See,
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for example, **brms**, which, like **rstanarm**, calls the **rstan** package
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internally to use [Stan](http://mc-stan.org/)'s MCMC sampler.
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internally to use [Stan](https://mc-stan.org/)'s MCMC sampler.
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```{r, mtcars}
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head(mtcars) # see help("mtcars")
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**Documentation:**
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* `help("MCMC-intervals")`
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* [mc-stan.org/bayesplot/reference/MCMC-intervals](http://mc-stan.org/bayesplot/reference/MCMC-intervals.html)
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* [mc-stan.org/bayesplot/reference/MCMC-intervals](https://mc-stan.org/bayesplot/reference/MCMC-intervals.html)
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------
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**Documentation:**
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* `help("MCMC-distributions")`
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* [mc-stan.org/bayesplot/reference/MCMC-distributions](http://mc-stan.org/bayesplot/reference/MCMC-distributions.html)
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* [mc-stan.org/bayesplot/reference/MCMC-distributions](https://mc-stan.org/bayesplot/reference/MCMC-distributions.html)
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------
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Various functions are available for plotting bivariate marginal posterior
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distributions. Some of these functions also take optional arguments
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for adding MCMC diagnostic information to the plots. That additional functionality
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is discussed in the separate [_Visual MCMC diagnostics_](http://mc-stan.org/bayesplot/articles/visual-mcmc-diagnostics.html)
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is discussed in the separate [_Visual MCMC diagnostics_](https://mc-stan.org/bayesplot/articles/visual-mcmc-diagnostics.html)
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vignette.
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**Documentation:**
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* `help("MCMC-scatterplots")`
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* [mc-stan.org/bayesplot/reference/MCMC-scatterplots](http://mc-stan.org/bayesplot/reference/MCMC-scatterplots.html)
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* [mc-stan.org/bayesplot/reference/MCMC-scatterplots](https://mc-stan.org/bayesplot/reference/MCMC-scatterplots.html)
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------
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controlling how the draws should be split between the plots above and below the
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diagonal (see the documentation for the `condition` argument), but they are more
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useful when MCMC diagnostic information is included. This is discussed in the
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[_Visual MCMC diagnostics_](http://mc-stan.org/bayesplot/articles/visual-mcmc-diagnostics.html)
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[_Visual MCMC diagnostics_](https://mc-stan.org/bayesplot/articles/visual-mcmc-diagnostics.html)
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vignette.
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Trace plots are time series plots of Markov chains. In this vignette
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we show the standard trace plots that **bayesplot** can make. For models
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fit using any Stan interface (or Hamiltonian Monte Carlo in general), the
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[_Visual MCMC diagnostics_](http://mc-stan.org/bayesplot/articles/visual-mcmc-diagnostics.html)
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[_Visual MCMC diagnostics_](https://mc-stan.org/bayesplot/articles/visual-mcmc-diagnostics.html)
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vignette provides an example of also adding information about divergences
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to trace plots.
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**Documentation:**
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* `help("MCMC-traces")`
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* [mc-stan.org/bayesplot/reference/MCMC-traces](http://mc-stan.org/bayesplot/reference/MCMC-traces.html)
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* [mc-stan.org/bayesplot/reference/MCMC-traces](https://mc-stan.org/bayesplot/reference/MCMC-traces.html)
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-------
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Gabry, J., and Goodrich, B. (2017). rstanarm: Bayesian Applied Regression
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Modeling via Stan. R package version 2.15.3.
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http://mc-stan.org/rstanarm, https://CRAN.R-project.org/package=rstanarm
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https://mc-stan.org/rstanarm, https://CRAN.R-project.org/package=rstanarm
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Gabry, J. , Simpson, D. , Vehtari, A. , Betancourt, M. and Gelman, A. (2019),
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Visualization in Bayesian workflow. _J. R. Stat. Soc. A_, 182: 389-402.
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Stan Development Team. (2017). *Stan Modeling Language Users
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Guide and Reference Manual*. http://mc-stan.org/users/documentation/
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Guide and Reference Manual*. https://mc-stan.org/users/documentation/

vignettes/visual-mcmc-diagnostics.Rmd

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divergent transitions and on the `n_eff` and `Rhat` statistics that help you
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determine that the chains have mixed well. Plots of parameter estimates
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from MCMC draws are covered in the separate vignette
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[_Plotting MCMC draws_](http://mc-stan.org/bayesplot/articles/plotting-mcmc-draws.html),
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[_Plotting MCMC draws_](https://mc-stan.org/bayesplot/articles/plotting-mcmc-draws.html),
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and graphical posterior predictive model checking is covered in the
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[_Graphical posterior predictive checks_](http://mc-stan.org/bayesplot/articles/graphical-ppcs.html)
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[_Graphical posterior predictive checks_](https://mc-stan.org/bayesplot/articles/graphical-ppcs.html)
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vignette.
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Note that most of these plots can also be browsed interactively using the
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[shinystan](http://mc-stan.org/shinystan/) package.
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[shinystan](https://mc-stan.org/shinystan/) package.
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### Setup
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parametrization fit. Those are serious business and in most cases indicate that
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[Divergent transitions after warmup](http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup).
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[Divergent transitions after warmup](https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup).
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We'll have a look at diagnosing the source of the divergences first and then
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dive into some diagnostics that should be checked even if there are no warnigns
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## Diagnostics for the No-U-Turn Sampler
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The No-U-Turn Sampler (NUTS, Hoffman and Gelman, 2014) is the variant of
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Hamiltonian Monte Carlo (HMC) used by [Stan](http://mc-stan.org/) and the
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Hamiltonian Monte Carlo (HMC) used by [Stan](https://mc-stan.org/) and the
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various R packages that depend on Stan for fitting Bayesian models.
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The **bayesplot** package has special functions for visualizing some of the
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unique diagnostics permitted by HMC, and NUTS in particular. See Betancourt
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* `help("MCMC-nuts")`
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* [mc-stan.org/bayesplot/reference/MCMC-nuts](http://mc-stan.org/bayesplot/reference/MCMC-nuts.html)
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* [mc-stan.org/bayesplot/reference/MCMC-nuts](https://mc-stan.org/bayesplot/reference/MCMC-nuts.html)
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In addition to the NUTS-specific plotting functions, some of the general
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[_Plotting MCMC draws_](http://mc-stan.org/bayesplot/articles/plotting-mcmc-draws.html)
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[_Plotting MCMC draws_](https://mc-stan.org/bayesplot/articles/plotting-mcmc-draws.html)
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vignette also take optional arguments that can be used to display important
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HMC/NUTS diagnostic information. We'll see examples of this in the next
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section on divergenent transitions.
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functions for visualizing Markov chain Monte Carlo (MCMC) diagnostics after
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fitting a Bayesian model. MCMC draws from any package can be used, although
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there are a few diagnostic plots that we will see later in this vignette that
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are specifically intended to be used for [Stan](http://mc-stan.org/) models (or
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are specifically intended to be used for [Stan](https://mc-stan.org/) models (or
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**Documentation:**
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* `help("MCMC-diagnostics")`
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* [mc-stan.org/bayesplot/reference/MCMC-diagnostics](http://mc-stan.org/bayesplot/reference/MCMC-diagnostics.html)
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* [mc-stan.org/bayesplot/reference/MCMC-diagnostics](https://mc-stan.org/bayesplot/reference/MCMC-diagnostics.html)
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Gabry, J., and Goodrich, B. (2018). rstanarm: Bayesian Applied Regression
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Modeling via Stan. R package version 2.17.4.
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http://mc-stan.org/rstanarm
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https://mc-stan.org/rstanarm
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Gabry, J. , Simpson, D. , Vehtari, A. , Betancourt, M. and Gelman, A. (2019),
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Visualization in Bayesian workflow. _J. R. Stat. Soc. A_, 182: 389-402.
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Educational and Behavioral Statistics*. 6:377--401.
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Stan Development Team. (2018). *Stan Modeling Language Users
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Guide and Reference Manual*. http://mc-stan.org/users/documentation/
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Guide and Reference Manual*. https://mc-stan.org/users/documentation/
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Stan Development Team. (2018). RStan: the R interface to Stan. R package version 2.17.3.
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http://mc-stan.org/rstan
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https://mc-stan.org/rstan

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