Trace and rank plots of MCMC draws

Trace and rank plots of MCMC draws. See the Plot Descriptions section, below, for details.

mcmc_trace(
  x,
  pars = character(),
  regex_pars = character(),
  transformations = list(),
  ...,
  facet_args = list(),
  n_warmup = 0,
  iter1 = 0,
  window = NULL,
  size = NULL,
  np = NULL,
  np_style = trace_style_np(),
  divergences = NULL
)

mcmc_trace_highlight(
  x,
  pars = character(),
  regex_pars = character(),
  transformations = list(),
  ...,
  facet_args = list(),
  n_warmup = 0,
  window = NULL,
  size = NULL,
  alpha = 0.2,
  highlight = 1
)

trace_style_np(div_color = "red", div_size = 0.25, div_alpha = 1)

mcmc_rank_overlay(
  x,
  pars = character(),
  regex_pars = character(),
  transformations = list(),
  facet_args = list(),
  ...,
  n_bins = 20,
  ref_line = FALSE
)

mcmc_rank_hist(
  x,
  pars = character(),
  regex_pars = character(),
  transformations = list(),
  ...,
  facet_args = list(),
  n_bins = 20,
  ref_line = FALSE
)

mcmc_rank_ecdf(
  x,
  pars = character(),
  regex_pars = character(),
  transformations = list(),
  ...,
  K = NULL,
  facet_args = list(),
  prob = 0.99,
  plot_diff = FALSE,
  interpolate_adj = NULL
)

mcmc_trace_data(
  x,
  pars = character(),
  regex_pars = character(),
  transformations = list(),
  ...,
  highlight = NULL,
  n_warmup = 0,
  iter1 = 0
)

Arguments

x

An object containing MCMC draws:

• A 3-D array, matrix, list of matrices, or data frame. The MCMC-overview page provides details on how to specify each these.

• A draws object from the posterior package (e.g., draws_array, draws_rvars, etc.).

• An object with an as.array() method that returns the same kind of 3-D array described on the MCMC-overview page.

pars

An optional character vector of parameter names. If neither pars nor regex_pars is specified then the default is to use all parameters. As of version 1.7.0, bayesplot also supports 'tidy' parameter selection by specifying pars = vars(...), where ... is specified the same way as in dplyr::select(...) and similar functions. Examples of using pars in this way can be found on the Tidy parameter selection page.

regex_pars

An optional regular expression to use for parameter selection. Can be specified instead of pars or in addition to pars. When using pars for tidy parameter selection, the regex_pars argument is ignored since select helpers perform a similar function.

transformations

Optionally, transformations to apply to parameters before plotting. If transformations is a function or a single string naming a function then that function will be used to transform all parameters. To apply transformations to particular parameters, the transformations argument can be a named list with length equal to the number of parameters to be transformed. Currently only univariate transformations of scalar parameters can be specified (multivariate transformations will be implemented in a future release). If transformations is a list, the name of each list element should be a parameter name and the content of each list element should be a function (or any item to match as a function via match.fun(), e.g. a string naming a function). If a function is specified by its name as a string (e.g. "log"), then it can be used to construct a new parameter label for the appropriate parameter (e.g. "log(sigma)"). If a function itself is specified (e.g. log or function(x) log(x)) then "t" is used in the new parameter label to indicate that the parameter is transformed (e.g. "t(sigma)").

Note: due to partial argument matching transformations can be abbreviated for convenience in interactive use (e.g., transform).

...

Currently ignored.

facet_args

A named list of arguments (other than facets) passed to ggplot2::facet_wrap() or ggplot2::facet_grid() to control faceting. Note: if scales is not included in facet_args then bayesplot may use scales="free" as the default (depending on the plot) instead of the ggplot2 default of scales="fixed".

n_warmup

An integer; the number of warmup iterations included in x. The default is n_warmup = 0, i.e. to assume no warmup iterations are included. If n_warmup > 0 then the background for iterations 1:n_warmup is shaded gray.

iter1

An integer; the iteration number of the first included draw (default is 0). This can be used to make it more obvious that the warmup iterations have been discarded from the traceplot. It cannot be specified if n_warmup is also set to a positive value.

window

An integer vector of length two specifying the limits of a range of iterations to display.

size

An optional value to override the default line size for mcmc_trace() or the default point size for mcmc_trace_highlight().

np

For models fit using NUTS (more generally, any symplectic integrator), an optional data frame providing NUTS diagnostic information. The data frame should be the object returned by nuts_params() or one with the same structure. If np is specified then tick marks are added to the bottom of the trace plot indicating within which iterations there was a divergence (if there were any). See the end of the Examples section, below.

np_style

A call to the trace_style_np() helper function to specify arguments controlling the appearance of tick marks representing divergences (if the np argument is specified).

divergences

Deprecated. Use the np argument instead.

alpha

For mcmc_trace_highlight(), passed to ggplot2::geom_point() to control the transparency of the points for the chains not highlighted.

highlight

For mcmc_trace_highlight(), an integer specifying one of the chains that will be more visible than the others in the plot.

div_color, div_size, div_alpha

Optional arguments to the trace_style_np() helper function that are eventually passed to ggplot2::geom_rug() if the np argument is also specified. They control the color, size, and transparency specifications for showing divergences in the plot. The default values are displayed in the Usage section above.

n_bins

For the rank plots, the number of bins to use for the histogram of rank-normalized MCMC samples. Defaults to 20.

ref_line

For the rank plots, whether to draw a horizontal line at the average number of ranks per bin. Defaults to FALSE.

K

An optional integer defining the number of equally spaced evaluation points for the ECDF. Reducing K when using interpolate_adj = FALSE makes computing the confidence bands faster. For ppc_pit_ecdf and ppc_pit_ecdf_grouped, defaults to ncol(yrep) + 1, or length(pit) if PIT values are supplied. For mcmc_rank_ecdf defaults to the number of iterations per chain in x.

prob

For mcmc_rank_ecdf(), a value between 0 and 1 specifying the desired simultaneous confidence of the confidence bands to be drawn for the rank ECDF plots.

plot_diff

For mcmc_rank_ecdf(), a boolean specifying if the difference between the observed rank ECDFs and the theoretical expectation should be drawn instead of the unmodified rank ECDF plots.

interpolate_adj

A boolean defining if the simultaneous confidence bands should be interpolated based on precomputed values rather than computed exactly. Computing the bands may be computationally intensive and the approximation gives a fast method for assessing the ECDF trajectory. The default is to use interpolation if K is greater than 200.

Value

The plotting functions return a ggplot object that can be further customized using the ggplot2 package. The functions with suffix _data() return the data that would have been drawn by the plotting function.

mcmc_trace_data() returns the data for the trace and rank plots in the same data frame.

Plot Descriptions

mcmc_trace()

Standard trace plots of MCMC draws. For models fit using NUTS, the np argument can be used to also show divergences on the trace plot.

mcmc_trace_highlight()

Traces are plotted using points rather than lines and the opacity of all chains but one (specified by the highlight argument) is reduced.

mcmc_rank_hist()

Whereas traditional trace plots visualize how the chains mix over the course of sampling, rank histograms visualize how the values from the chains mix together in terms of ranking. An ideal plot would show the rankings mixing or overlapping in a uniform distribution. See Vehtari et al. (2019) for details.

mcmc_rank_overlay()

Ranks from mcmc_rank_hist() are plotted using overlaid lines in a single panel.

mcmc_rank_ecdf()

The ECDFs of the ranks from mcmc_rank_hist() are plotted with the simultaneous confidence bands with a coverage determined by prob, that is, bands that completely cover all of the rank ECDFs with the probability prob. If plot_diff = TRUE, the difference between the observed rank ECDFs and the theoretical expectation for samples originating from the same distribution is drawn. See Säilynoja et al. (2021) for details.

References

Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., Bürkner, P. (2019). Rank-normalization, folding, and localization: An improved R-hat for assessing convergence of MCMC. arXiv preprint.

Säilynoja, T., Bürkner, P., Vehtari, A. (2021). Graphical Test for Discrete Uniformity and its Applications in Goodness of Fit Evaluation and Multiple Sample Comparison arXiv preprint.

See also

Other MCMC: MCMC-combos, MCMC-diagnostics, MCMC-distributions, MCMC-intervals, MCMC-nuts, MCMC-overview, MCMC-parcoord, MCMC-recover, MCMC-scatterplots

Examples

# some parameter draws to use for demonstration
x <- example_mcmc_draws(chains = 4, params = 6)
dim(x)
#> [1] 250   4   6
dimnames(x)
#> $Iteration
#> NULL
#> 
#> $Chain
#> [1] "chain:1" "chain:2" "chain:3" "chain:4"
#> 
#> $Parameter
#> [1] "alpha"   "sigma"   "beta[1]" "beta[2]" "beta[3]" "beta[4]"
#> 

# trace plots of the betas
color_scheme_set("viridis")
mcmc_trace(x, regex_pars = "beta")

# \donttest{
color_scheme_set("viridisA")
mcmc_trace(x, regex_pars = "beta")


color_scheme_set("viridisC")
mcmc_trace(x, regex_pars = "beta")

# }

# mix color schemes
color_scheme_set("mix-blue-red")
mcmc_trace(x, regex_pars = "beta")


# use traditional ggplot discrete color scale
mcmc_trace(x, pars = c("alpha", "sigma")) +
 ggplot2::scale_color_discrete()
#> Scale for colour is already present.
#> Adding another scale for colour, which will replace the existing scale.


# zoom in on a window of iterations, increase line size,
# add tick marks, move legend to the top, add gray background
color_scheme_set("viridisA")
mcmc_trace(x[,, 1:4], window = c(100, 130), size = 1) +
  panel_bg(fill = "gray90", color = NA) +
  legend_move("top")


# Rank-normalized histogram plots. Instead of showing how chains mix over
# time, look at how the ranking of MCMC samples mixed between chains.
color_scheme_set("viridisE")
mcmc_rank_hist(x, "alpha")

mcmc_rank_hist(x, pars = c("alpha", "sigma"), ref_line = TRUE)

mcmc_rank_overlay(x, "alpha")


# ECDF and ECDF difference plots of the ranking of MCMC samples between chains.
# Provide 99% simultaneous confidence intervals for the chains sampling from
# the same distribution.
mcmc_rank_ecdf(x, prob = 0.99)

mcmc_rank_ecdf(x, prob = 0.99, plot_diff = TRUE)


# \dontrun{
# parse facet label text
color_scheme_set("purple")
p <- mcmc_trace(
  x,
  regex_pars = "beta\\[[1,3]\\]",
  facet_args = list(labeller = ggplot2::label_parsed)
)
p + facet_text(size = 15)


# mark first 100 draws as warmup
mcmc_trace(x, n_warmup = 100)


# plot as points, highlighting chain 2
color_scheme_set("brightblue")
mcmc_trace_highlight(x, pars = "sigma", highlight = 2, size = 2)


# for models fit using HMC/NUTS divergences can be displayed in the trace plot
library("rstanarm")
fit <- stan_glm(mpg ~ ., data = mtcars, refresh = 0,
  # next line to keep example fast and also ensure we get some divergences
                prior = hs(), iter = 400, adapt_delta = 0.8)
#> Warning: There were 21 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess

# extract draws using as.array (instead of as.matrix) to keep
# chains separate for trace plot
posterior <- as.array(fit)

# for stanfit and stanreg objects use nuts_params() to get the divergences
mcmc_trace(posterior, pars = "sigma", np = nuts_params(fit))


color_scheme_set("viridis")
mcmc_trace(
  posterior,
  pars = c("wt", "sigma"),
  size = 0.5,
  facet_args = list(nrow = 2),
  np = nuts_params(fit),
  np_style = trace_style_np(div_color = "black", div_size = 0.5)
)

# }