Compare the empirical distribution of the data y to the distributions of simulated/replicated data yrep from the posterior predictive distribution. See the Plot Descriptions section, below, for details.

ppc_data(y, yrep, group = NULL)

ppc_hist(y, yrep, ..., binwidth = NULL, freq = TRUE)

ppc_boxplot(y, yrep, ..., notch = TRUE, size = 0.5, alpha = 1)

ppc_freqpoly(y, yrep, ..., binwidth = NULL, freq = TRUE, size = 0.25,
  alpha = 1)

ppc_freqpoly_grouped(y, yrep, group, ..., binwidth = NULL, freq = TRUE,
  size = 0.25, alpha = 1)

ppc_dens(y, yrep, ..., trim = FALSE, size = 0.5, alpha = 1)

ppc_dens_overlay(y, yrep, ..., size = 0.25, alpha = 0.7, trim = FALSE,
  bw = "nrd0", adjust = 1, kernel = "gaussian", n_dens = 1024)

ppc_ecdf_overlay(y, yrep, ..., pad = TRUE, size = 0.25, alpha = 0.7)

ppc_violin_grouped(y, yrep, group, ..., probs = c(0.1, 0.5, 0.9), size = 1,
  alpha = 1, y_draw = c("violin", "points", "both"), y_size = 1,
  y_alpha = 1, y_jitter = 0.1)



A vector of observations. See Details.


An \(S\) by \(N\) matrix of draws from the posterior predictive distribution, where \(S\) is the size of the posterior sample (or subset of the posterior sample used to generate yrep) and \(N\) is the number of observations (the length of y). The columns of yrep should be in the same order as the data points in y for the plots to make sense. See Details for additional instructions.


A grouping variable (a vector or factor) the same length as y. Each value in group is interpreted as the group level pertaining to the corresponding value of y.


Currently unused.


An optional value used as the binwidth argument to geom_histogram to override the default binwidth.


For histograms, freq=TRUE (the default) puts count on the y-axis. Setting freq=FALSE puts density on the y-axis. (For many plots the y-axis text is off by default. To view the count or density labels on the y-axis see the yaxis_text convenience function.)


A logical scalar passed to geom_boxplot. Unlike for geom_boxplot, the default is notch=TRUE.

size, alpha

Passed to the appropriate geom to control the appearance of the yrep distributions.


A logical scalar passed to geom_density.

bw, adjust, kernel, n_dens

Optional arguments passed to density to override default kernel density estimation parameters. n_dens defaults to 1024.


A logical scalar passed to stat_ecdf.


A numeric vector passed to geom_violin's draw_quantiles argument to specify at which quantiles to draw horizontal lines. Set to NULL to remove the lines.


For ppc_violin_grouped, a string specifying how to draw y: "violin" (default), "points" (jittered points), or "both".

y_jitter, y_size, y_alpha

For ppc_violin_grouped, if y_draw is "points" or "both" then y_size, y_alpha, and y_jitter are passed to to the size, alpha, and width arguments of geom_jitter to control the appearance of y points. The default of y_jitter=NULL will let ggplot2 determine the amount of jitter.


A ggplot object that can be further customized using the ggplot2 package. The _data functions return the data that would have be drawn by the plotting function.


For Binomial data, the plots will typically be most useful if y and yrep contain the "success" proportions (not discrete "success" or "failure" counts).

Plot Descriptions

ppc_hist, ppc_freqpoly, ppc_dens, ppc_boxplot

A separate histogram, shaded frequency polygon, smoothed kernel density estimate, or box and whiskers plot is displayed for y and each dataset (row) in yrep. For these plots yrep should therefore contain only a small number of rows. See the Examples section.


A separate frequency polygon is plotted for each level of a grouping variable for y and each dataset (row) in yrep. For this plot yrep should therefore contain only a small number of rows. See the Examples section.

ppc_dens_overlay, ppc_ecdf_overlay

Kernel density or empirical CDF estimates of each dataset (row) in yrep are overlaid, with the distribution of y itself on top (and in a darker shade).


The density estimate of yrep within each level of a grouping variable is plotted as a violin with horizontal lines at notable quantiles. y is overlaid on the plot either as a violin, points, or both, depending on the y_draw argument.


Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B. (2013). Bayesian Data Analysis. Chapman & Hall/CRC Press, London, third edition. (Ch. 6)

See also

Other PPCs: PPC-discrete, PPC-errors, PPC-intervals, PPC-loo, PPC-overview, PPC-scatterplots, PPC-test-statistics


color_scheme_set("brightblue") y <- example_y_data() yrep <- example_yrep_draws() dim(yrep)
#> [1] 500 434
ppc_dens_overlay(y, yrep[1:25, ])
ppc_ecdf_overlay(y, yrep[sample(nrow(yrep), 25), ])
# for ppc_hist,dens,freqpoly,boxplot definitely use a subset yrep rows so # only a few (instead of nrow(yrep)) histograms are plotted ppc_hist(y, yrep[1:8, ])
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
color_scheme_set("red") ppc_boxplot(y, yrep[1:8, ])
# wizard hat plot color_scheme_set("blue") ppc_dens(y, yrep[200:202, ])
ppc_freqpoly(y, yrep[1:3,], alpha = 0.1, size = 1, binwidth = 5)
# if groups are different sizes then the 'freq' argument can be useful group <- example_group_data() ppc_freqpoly_grouped(y, yrep[1:3,], group) + yaxis_text()
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
ppc_freqpoly_grouped(y, yrep[1:3,], group, freq = FALSE) + yaxis_text()
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
# don't need to only use small number of rows for ppc_violin_grouped # (as it pools yrep draws within groups) color_scheme_set("gray") ppc_violin_grouped(y, yrep, group, size = 1.5)
ppc_violin_grouped(y, yrep, group, alpha = 0)
# change how y is drawn ppc_violin_grouped(y, yrep, group, alpha = 0, y_draw = "points", y_size = 1.5)
ppc_violin_grouped(y, yrep, group, alpha = 0, y_draw = "both", y_size = 1.5, y_alpha = 0.5, y_jitter = 0.33)