PPC distributions

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

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

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

ppc_ecdf_overlay_grouped(
  y,
  yrep,
  group,
  ...,
  discrete = FALSE,
  pad = TRUE,
  size = 0.25,
  alpha = 0.7
)

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

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

ppc_freqpoly(
  y,
  yrep,
  ...,
  binwidth = NULL,
  bins = NULL,
  freq = TRUE,
  size = 0.5,
  alpha = 1
)

ppc_freqpoly_grouped(
  y,
  yrep,
  group,
  ...,
  binwidth = NULL,
  bins = NULL,
  freq = TRUE,
  size = 0.5,
  alpha = 1
)

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

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
)

ppc_pit_ecdf(
  y,
  yrep,
  ...,
  pit = NULL,
  K = NULL,
  prob = 0.99,
  plot_diff = FALSE,
  interpolate_adj = NULL
)

ppc_pit_ecdf_grouped(
  y,
  yrep,
  group,
  ...,
  K = NULL,
  pit = NULL,
  prob = 0.99,
  plot_diff = FALSE,
  interpolate_adj = NULL
)

Arguments

y

A vector of observations. See Details.

yrep

An S by N matrix of draws from the posterior (or prior) predictive distribution. The number of rows, S, is the size of the posterior (or prior) sample used to generate yrep. The number of columns, N is the number of predicted observations (length(y)). The columns of yrep should be in the same order as the data points in y for the plots to make sense. See the Details and Plot Descriptions sections for additional advice specific to particular plots.

group

A grouping variable of the same length as y. Will be coerced to factor if not already a factor. Each value in group is interpreted as the group level pertaining to the corresponding observation.

...

Currently unused.

size, alpha

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

trim

A logical scalar passed to ggplot2::geom_density().

bw, adjust, kernel, n_dens

Optional arguments passed to stats::density() to override default kernel density estimation parameters. n_dens defaults to 1024.

discrete

For ppc_ecdf_overlay(), should the data be treated as discrete? The default is FALSE, in which case geom="line" is passed to ggplot2::stat_ecdf(). If discrete is set to TRUE then geom="step" is used.

pad

A logical scalar passed to ggplot2::stat_ecdf().

binwidth

Passed to ggplot2::geom_histogram() to override the default binwidth.

bins

Passed to ggplot2::geom_histogram() to override the default binwidth.

breaks

Passed to ggplot2::geom_histogram() as an alternative to binwidth.

freq

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.)

notch

For the box plot, a logical scalar passed to ggplot2::geom_boxplot(). Note: unlike geom_boxplot(), the default is notch=TRUE.

probs

A numeric vector passed to ggplot2::geom_violin()'s draw_quantiles argument to specify at which quantiles to draw horizontal lines. Set to NULL to remove the lines.

y_draw

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 ggplot2::geom_jitter() to control the appearance of y points. The default of y_jitter=NULL will let ggplot2 determine the amount of jitter.

pit

An optional vector of probability integral transformed values for which the ECDF is to be drawn. If NULL, PIT values are computed to y with respect to the corresponding values in yrep.

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

The desired simultaneous coverage level of the bands around the ECDF. A value in (0,1).

plot_diff

A boolean defining whether to plot the difference between the observed ECDF and the theoretical expectation for uniform PIT values rather than plotting the regular ECDF. The default is FALSE, but for large samples we recommend setting plot_diff=TRUE as the difference plot will visually show a more dynamic range.

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.

Details

For Binomial data, the plots may be more useful if the input contains 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.

ppc_freqpoly_grouped()

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_ecdf_overlay(), ppc_dens_overlay(), ppc_ecdf_overlay_grouped(), ppc_dens_overlay_grouped()

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). When using ppc_ecdf_overlay() with discrete data, set the discrete argument to TRUE for better results. For an example of ppc_dens_overlay() also see Gabry et al. (2019).

ppc_violin_grouped()

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.

ppc_pit_ecdf(), ppc_pit_ecdf_grouped()

The ECDF of the empirical PIT values of y computed with respect to the corresponding yrep values. 100 * prob% central simultaneous confidence intervals are provided to asses if y and yrep originate from the same distribution. The PIT values can also be provided directly as pit. See Säilynoja et al. (2021) for more details.

References

Gabry, J. , Simpson, D. , Vehtari, A. , Betancourt, M. and Gelman, A. (2019), Visualization in Bayesian workflow. J. R. Stat. Soc. A, 182: 389-402. doi:10.1111/rssa.12378. (journal version, arXiv preprint, code on GitHub)

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.

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-censoring, PPC-discrete, PPC-errors, PPC-intervals, PPC-loo, PPC-overview, PPC-scatterplots, PPC-test-statistics

Examples

color_scheme_set("brightblue")
y <- example_y_data()
yrep <- example_yrep_draws()
group <- example_group_data()
dim(yrep)
#> [1] 500 434

ppc_dens_overlay(y, yrep[1:25, ])

# \donttest{
# ppc_ecdf_overlay with continuous data (set discrete=TRUE if discrete data)
ppc_ecdf_overlay(y, yrep[sample(nrow(yrep), 25), ])


# ECDF and ECDF difference plot of the PIT values of y compared to yrep
# with 99% simultaneous confidence bands.
ppc_pit_ecdf(y, yrep, prob = 0.99, plot_diff = FALSE)

ppc_pit_ecdf(y, yrep, prob = 0.99, plot_diff = TRUE)

# }

# 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`.

# \donttest{
color_scheme_set("red")
ppc_boxplot(y, yrep[1:8, ])


# wizard hat plot
color_scheme_set("blue")
ppc_dens(y, yrep[200:202, ])

# }

# \donttest{
# frequency polygons
ppc_freqpoly(y, yrep[1:3, ], alpha = 0.1, size = 1, binwidth = 5)


ppc_freqpoly_grouped(y, yrep[1:3, ], group) + yaxis_text()
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


# if groups are different sizes then the 'freq' argument can be useful
ppc_freqpoly_grouped(y, yrep[1:3, ], group, freq = FALSE) + yaxis_text()
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

# }

# density and distribution overlays by group
ppc_dens_overlay_grouped(y, yrep[1:25, ], group = group)


ppc_ecdf_overlay_grouped(y, yrep[1:25, ], group = group)


# \donttest{
# ECDF difference plots of the PIT values by group
# with 99% simultaneous confidence bands.
ppc_pit_ecdf_grouped(y, yrep, group=group, prob=0.99, plot_diff = TRUE)

# }

# \donttest{
# 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
)

# }