The distribution of a test statistic T(yrep), or a pair of test statistics, over the simulated datasets in yrep, compared to the observed value T(y) computed from the data y. See the Plot Descriptions and Details sections, below.

ppc_stat(y, yrep, stat = "mean", ..., binwidth = NULL, freq = TRUE)

ppc_stat_grouped(y, yrep, group, stat = "mean", ..., facet_args = list(),
  binwidth = NULL, freq = TRUE)

ppc_stat_freqpoly_grouped(y, yrep, group, stat = "mean", ...,
  facet_args = list(), binwidth = NULL, freq = TRUE)

ppc_stat_2d(y, yrep, stat = c("mean", "sd"), ..., size = 2.5, alpha = 0.7)



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 single function or a string naming a function, except for ppc_stat_2d which requires a vector of exactly two functions or function names. In all cases the function(s) should take a vector input and return a scalar test statistic. If specified as a string (or strings) then the legend will display function names. If specified as a function (or functions) then generic naming is used in the legend.


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 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.


A named list of arguments (other than facets) passed to facet_wrap or facet_grid to control faceting.

size, alpha

Arguments passed to geom_point to control the appearance of scatterplot points.


A ggplot object that can be further customized using the ggplot2 package.


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


A histogram of the distribution of a test statistic computed by applying stat to each dataset (row) in yrep. The value of the statistic in the observed data, stat(y), is overlaid as a vertical line.


The same as ppc_stat, but a separate plot is generated for each level of a grouping variable. In the case of ppc_stat_freqpoly_grouped the plots are frequency polygons rather than histograms.


A scatterplot showing the joint distribution of two test statistics computed over the datasets (rows) in yrep. The value of the statistics in the observed data is overlaid as large point.


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-distributions, PPC-errors, PPC-intervals, PPC-loo, PPC-overview, PPC-scatterplots


y <- example_y_data() yrep <- example_yrep_draws() ppc_stat(y, yrep)
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
ppc_stat(y, yrep, stat = "sd") + legend_none()
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
ppc_stat_2d(y, yrep)
ppc_stat_2d(y, yrep, stat = c("median", "mean")) + legend_move("bottom")
color_scheme_set("teal") group <- example_group_data() ppc_stat_grouped(y, yrep, group)
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
color_scheme_set("mix-red-blue") ppc_stat_freqpoly_grouped(y, yrep, group, facet_args = list(nrow = 2))
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
# use your own function to compute test statistics color_scheme_set("brightblue") q25 <- function(y) quantile(y, 0.25) ppc_stat(y, yrep, stat = "q25") # legend includes function name
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
# can define the function in the 'stat' argument but then # the legend doesn't include a function name ppc_stat(y, yrep, stat = function(y) quantile(y, 0.25))
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.