Diagnostic plots for the No-U-Turn-Sampler (NUTS), the default MCMC algorithm used by Stan. See the Plot Descriptions section, below.

mcmc_nuts_acceptance(x, lp, chain = NULL, ..., binwidth = NULL)

mcmc_nuts_divergence(x, lp, chain = NULL, ...)

mcmc_nuts_stepsize(x, lp, chain = NULL, ...)

mcmc_nuts_treedepth(x, lp, chain = NULL, ...)

mcmc_nuts_energy(x, ..., binwidth = NULL, alpha = 0.5,
  merge_chains = FALSE)



A molten data frame of NUTS sampler parameters, either created by nuts_params or in the same form as the object returned by nuts_params.


A molten data frame of draws of the log-posterior or, more commonly, of a quantity equal to the log-posterior up to a constant. lp should either be created via log_posterior or be an object with the same form as the object returned by log_posterior.


A positive integer for selecting a particular chain. The default (NULL) is to merge the chains before plotting. If chain = k then the plot for chain k is overlaid (in a darker shade but with transparency) on top of the plot for all chains. The chain argument is not used by mcmc_nuts_energy.


Currently ignored.


An optional value passed to geom_histogram to override the default binwidth.


For mcmc_nuts_energy only, the transparency (alpha) level in [0,1] used for the overlaid histogram.


For mcmc_nuts_energy only, should all chains be merged or displayed separately? The default is FALSE, i.e., to show the chains separately.


A gtable object (the result of calling arrangeGrob) created from several ggplot objects, except for mcmc_nuts_energy, which returns a ggplot object.

Quick Definitions

For more details see Stan Development Team (2016) and Betancourt (2017).

  • accept_stat__: the average acceptance probabilities of all possible samples in the proposed tree.

  • divergent__: the number of leapfrog transitions with diverging error. Because NUTS terminates at the first divergence this will be either 0 or 1 for each iteration.

  • stepsize__: the step size used by NUTS in its Hamiltonian simulation.

  • treedepth__: the depth of tree used by NUTS, which is the log (base 2) of the number of leapfrog steps taken during the Hamiltonian simulation.

  • energy__: the value of the Hamiltonian (up to an additive constant) at each iteration.

Plot Descriptions


Three plots:

  • Histogram of accept_stat__ with vertical lines indicating the mean (solid line) and median (dashed line).

  • Histogram of lp__ with vertical lines indicating the mean (solid line) and median (dashed line).

  • Scatterplot of accept_stat__ vs lp__.


Two plots:

  • Violin plots of lp__|divergent__=1 and lp__|divergent__=0.

  • Violin plots of accept_stat__|divergent__=1 and accept_stat__|divergent__=0.


Two plots:

  • Violin plots of lp__ by chain ordered by stepsize__ value.

  • Violin plots of accept_stat__ by chain ordered by stepsize__ value.


Three plots:

  • Violin plots of lp__ by value of treedepth__.

  • Violin plots of accept_stat__ by value of treedepth__.

  • Histogram of treedepth__.


Overlaid histograms showing energy__ vs the change in energy__. See Betancourt (2016) for details.


Betancourt, M. (2017). A conceptual introduction to Hamiltonian Monte Carlo. https://arxiv.org/abs/1701.02434

Betancourt, M. and Girolami, M. (2013). Hamiltonian Monte Carlo for hierarchical models. https://arxiv.org/abs/1312.0906

Hoffman, M. D. and Gelman, A. (2014). The No-U-Turn Sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research. 15:1593--1623.

Stan Development Team. (2016). Stan Modeling Language Users Guide and Reference Manual. http://mc-stan.org/documentation/

See also

  • The Visual MCMC Diagnostics vignette.

  • Several other plotting functions in the bayesplot package are not NUTS-specific but take optional extra arguments if the model was fit using NUTS:

    • mcmc_trace: show divergences as tick marks below the trace plot.

    • mcmc_parcoord: change the color/size/transparency of lines correspondending to divergences.

    • mcmc_scatter: change the color/size/shape of points corresponding to divergences.

    • mcmc_pairs: change the color/size/shape of points corresponding divergences and/or max treedepth saturation.


fit <- stan_glm(mpg ~ wt + am, data = mtcars, iter = 1000)
np <- nuts_params(fit)
lp <- log_posterior(fit)

mcmc_nuts_acceptance(np, lp)
mcmc_nuts_acceptance(np, lp, chain = 2)

mcmc_nuts_divergence(np, lp)
mcmc_nuts_stepsize(np, lp)
mcmc_nuts_treedepth(np, lp)

mcmc_nuts_energy(np, merge_chains = TRUE, binwidth = .15)
mcmc_nuts_energy(np) +
 facet_wrap(~ Chain, nrow = 1) +
 coord_fixed(ratio = 150) +
 ggtitle("NUTS Energy Diagnostic")
# }