---
title: "Slab + interval stats and geoms"
author: "Matthew Kay"
date: "`r Sys.Date()`"
output: 
  rmarkdown::html_vignette:
    toc: true
    df_print: kable
vignette: >
  %\VignetteIndexEntry{Slab + interval stats and geoms}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---
  
<style type="text/css">
.kable-table table {
  margin-left: 0;
}
img {
  border: none;
}
</style>

```{r chunk_options, include=FALSE}
tiny_width = small_width = med_width = 6.75
tiny_height = small_height = med_height = 4.5
large_width = 8; large_height = 5.25

knitr::opts_chunk$set(
  fig.width = small_width,
  fig.height = small_height
)
if (capabilities("cairo") && Sys.info()[['sysname']] != "Darwin") {
  knitr::opts_chunk$set(
    dev.args = list(png = list(type = "cairo"))
  )
}
```

## Introduction
  
This vignette describes the slab+interval geoms and stats in `ggdist`. This is a flexible family of stats and geoms designed to make plotting distributions (such as priors and posteriors in Bayesian models, or even sampling distributions from other models) straightforward, and support a range of useful plots, including intervals, eye plots (densities + intervals), CCDF bar plots (complementary cumulative distribution functions + intervals), gradient plots, and histograms.

## Setup
  
The following libraries are required to run this vignette:
  
```{r setup, message = FALSE, warning = FALSE}
library(dplyr)
library(tidyr)
library(distributional)
library(ggdist)
library(ggplot2)
library(cowplot)

theme_set(theme_ggdist())
```

```{r hidden_options, include=FALSE}
.old_options = options(width = 120)
```


## Roadmap: It all starts with "slabinterval"

```{r slabinterval_family, fig.height = 5.5, fig.width = 7, echo = FALSE}
dists_df = tibble(
  # enforce order
  geom = rev(c(
    "halfeye", 
    "eye",
    "gradientinterval", 
    "ccdfinterval", 
    "cdfinterval",
    "interval",
    "pointinterval",
    "slab",
    "dots",
    "dotsinterval",
    "histinterval"
    )) %>%
    factor(., levels = .),
  dist = "norm",
  args = list(list(4, 1))
)

hist_df = tibble(
  geom = "histinterval",
  x = qnorm(ppoints(1000), 4, 1),
  dist = NA,
  args = NA
)

dists_plot = dists_df %>%
  ggplot(aes(y = geom, dist = dist, args = args)) +
  geom_blank() + # ensures order
  stat_dist_eye(data = . %>% filter(geom == "eye")) +
  stat_dist_halfeye(data = . %>% filter(geom == "halfeye"), position = position_nudge(y = - 0.2)) +
  stat_dist_gradientinterval(data = . %>% filter(geom == "gradientinterval"), scale = .5) +
  stat_dist_ccdfinterval(data = . %>% filter(geom == "ccdfinterval"), scale = .5) +
  stat_dist_cdfinterval(data = . %>% filter(geom == "cdfinterval"), scale = .5) +
  stat_interval(aes(x = x, y = "interval"), data = hist_df, color = "gray65", alpha = 1/3, size = 10,
    position = position_nudge(y = -.1)) +
  stat_pointinterval(aes(x = x, y = "pointinterval"), data = hist_df) +
  stat_dist_slab(data = . %>% filter(geom == "slab"), position = position_nudge(y = - 0.2)) +
  stat_dist_dotsinterval(data = . %>% filter(geom == "dotsinterval"), position = position_nudge(y = - 0.3)) +
  stat_dist_dots(data = . %>% filter(geom == "dots"), position = position_nudge(y = - 0.3)) +
  stat_histinterval(aes(x = x), data = hist_df, position = position_nudge(y = - 0.4)) +
  scale_slab_alpha_continuous(guide = FALSE) +
  scale_x_continuous(limits = c(0,8), expand = c(0,0)) +
  labs(
    subtitle = "The stat_slabinterval / geom_slabinterval family",
    x = NULL,
    y = NULL
  )

annotation_plot = tribble(
    ~geom,                 ~prefix,
    "halfeye",          c("stat_...", "stat_dist_..."),
    "eye",              c("stat_...", "stat_dist_..."),
    "gradientinterval", c("stat_...", "stat_dist_..."),
    "ccdfinterval",     c("stat_...", "stat_dist_..."),
    "cdfinterval",      c("stat_...", "stat_dist_..."),
    "interval",         c("stat_...", "stat_dist_...", "geom_..."),
    "pointinterval",    c("stat_...", "stat_dist_...", "geom_..."),
    "slab",             c("stat_...", "stat_dist_...", "geom_..."),
    "dotsinterval",     c("stat_...", "stat_dist_...", "geom_..."),
    "dots",             c("stat_...", "stat_dist_...", "geom_..."),
    "histinterval",     c("stat_..."),
  ) %>%
  unnest(prefix) %>%
  mutate(
    geom = factor(geom, levels = levels(dists_df$geom)),
    prefix = factor(prefix, levels = c("stat_...", "stat_dist_...", "geom_..."))
  ) %>%
  ggplot(aes(x = prefix, y = geom)) +
  geom_hline(aes(yintercept = as.numeric(geom) - .1), color = "gray80", data = . %>% filter(prefix == "stat_...")) +
  geom_point(size = 5, color = "gray65", position = position_nudge(y = -.1)) +
  scale_x_discrete(position = "top") +
  scale_y_discrete(breaks = NULL, expand = c(0,.6)) +
  labs(y = NULL, x = NULL) +
  theme(axis.line.x = element_blank(), axis.line.y = element_blank(), axis.ticks = element_blank()) 

plot_grid(ncol = 2, align = "h", rel_widths = c(0.65, 0.35),
  dists_plot,
  annotation_plot
)
```

`ggdist` has a pantheon of geoms and stats that stem from a common root: `geom_slabinterval()` and `stat_slabinterval()`. These geoms consist of a "slab" (say, a density or a CDF), one or more intervals, and a point summary. These components may be computed in a number of different ways, and different variants of the geom will or will not include all components. 

Using `geom_slabinterval()` and `stat_slabinterval()` directly is not necessarily advisable: they are highly configurable on their own, but this configurability requires remembering a bunch of combinations of options to use. Instead, ggdist contains a number of pre-configured, easier-to-remember stats and geoms built on top of the slabinterval. These follow the following naming scheme:

`[geom|stat|stat_dist]_[name]`

For example, `stat_dist_eye()`, `stat_eye()`, `stat_pointinterval()`, `geom_pointinterval()`, etc. The naming scheme works as follows:

* Geoms starting with `geom_` are meant to be used on already-summarized data (typically data summarized into intervals): things like `geom_pointinterval()` and `geom_interval()`.
* Stats starting with `stat_` are meant to be used on sample data; e.g. draws from a posterior distribution (or any other distribution, really). These stats compute relevant summaries (densities, CDFs, points, and/or intervals) before forwarding the summaries to their geom. Some have geom counterparts (e.g. `stat_interval()` corresponds to `geom_interval()`, except the former applies to sample data and the latter to already-summarized data). Many of these stats do not currently have geom counterparts (e.g. `stat_ccdfinterval()`), as they are primarily differentiated based on what kind of statistical summary they compute. If you've already computed a function (such as a density or CDF), you can just use `geom_slabinterval()` directly.
* Stats starting with `stat_dist_` can be used to create slab+interval geoms for analytical distributions. They take either [distributional](https://pkg.mitchelloharawild.com/distributional/) objects or distribution names (the `dist` aesthetic) and arguments (the `args` aesthetic or `arg1`, ... `arg9` aesthetics) and compute the relevant slabs and intervals. Thus, where `stat_eye()` makes an eye plot for sample data, `stat_dist_eye()` makes an eye plot for an analytical distribution.

All slabinterval geoms can be plotted horizontally or vertically. Depending on how aesthetics are mapped, they will attempt to automatically determine the orientation; if this does not produce the correct result, the orientation can be overridden by setting `orientation = "horizontal"` or `orientation = "vertical"`.

We'll start with one of the most common existing use cases for these kinds geoms: eye plots.

## Eye plots and half-eye plots 

### On sample data: `stat_[half]eye`

Eye plots combine densities (as violins) with intervals to give a more detailed picture of uncertainty than is available just by looking at intervals. 

For these first few demos we'll use these data:

```{r sample_data}
set.seed(1234)
df = tribble(
    ~group, ~subgroup, ~value,
    "a",          "h", rnorm(1000, mean = 5),
    "b",          "h", rnorm(1000, mean = 7, sd = 1.5),
    "c",          "h", rnorm(1000, mean = 8),
    "c",          "i", rnorm(1000, mean = 9),
    "c",          "j", rnorm(1000, mean = 7)
  ) %>%
  unnest(value)
```

We can summarize it at the group level using an eye plot with `stat_eye()` (ignoring subgroups for now):

```{r group_eye, fig.width = small_height, fig.height = small_height}
df %>%
  ggplot(aes(y = group, x = value)) +
  stat_eye() +
  ggtitle("stat_eye()")
```

Users of older versions of `tidybayes` (which used to contain the `ggdist` geoms) might have used `geom_eye()`, which is the older spelling of `stat_eye()`. Due to the name standardization in version 2 of `tidybayes` (see the description above), `stat_eye()` is now the preferred spelling. `geom_eye()` will continue to work for now, but is deprecated and may throw a warning in future versions.

We can also use `stat_halfeye()` instead to get densities instead of violins:

```{r group_halfeye, fig.width = small_height, fig.height = small_height}
df %>%
  ggplot(aes(y = group, x = value)) +
  stat_halfeye() +
  ggtitle("stat_halfeye()")
```

Or use the `side` parameter to more finely control where the slab (in this case, the density) is drawn:

```{r eye_side, fig.width = med_width, fig.height = small_height}
p = df %>%
  ggplot(aes(x = group, y = value)) +
  panel_border()

plot_grid(ncol = 3, align = "hv",
  p + stat_eye(side = "left") + labs(title = "stat_eye()", subtitle = "side = 'left'"),
  p + stat_eye(side = "both") + labs(subtitle = "side = 'both'"),
  p + stat_eye(side = "right")  + labs(subtitle = "side = 'right'")
)
```

Note how the above chart was drawn vertically instead of horizontally: all slabinterval geoms automatically detect their orientation based on the input data. For example, if you use a factor on one axis (say the `x` axis below), the geom will be drawn along the other axis:

```{r halfeyeh, fig.width = small_height, fig.height = small_height}
df %>%
  ggplot(aes(x = group, y = value)) +
  stat_halfeye() +
  ggtitle("stat_halfeye()")
```

If automatic detection of the desired axis fails, you can specify it manually; e.g. with `stat_halfeye(orientation = 'vertical')` or `stat_halfeye(orientation = 'horizontal')`.

The `side` parameter works for horizontal geoms as well. `"top"` and `"right"` are considered synonyms, as are `"bottom"` and `"left"`; either form works with both horizontal and vertical versions of the geoms:

```{r eyeh_side, fig.width = med_width, fig.height = small_height}
p = df %>%
  ggplot(aes(x = value, y = group)) +
  panel_border()

plot_grid(ncol = 3, align = "hv", 
  # side = "left" would give the same result
  p + stat_eye(side = "left") + ggtitle("stat_eye()") + labs(subtitle = "side = 'bottom'"),
  p + stat_eye(side = "both") + labs(subtitle = "side = 'both'"),
  # side = "right" would give the same result
  p + stat_eye(side = "right") + labs(subtitle = "side = 'top'")
)
```

Eye plots are also designed to support dodging through the standard mechanism of `position = "dodge"`. 
Unlike with geom_violin(), densities in groups that are not dodged (here, 'a' and 'b') have the same area and max width as those in groups that are dodged ('c'):

```{r eye_dodge}
df %>%
  ggplot(aes(x = group, y = value, fill = subgroup)) +
  stat_eye(position = "dodge") +
  ggtitle("stat_eye(position = 'dodge')")
```

Dodging works whether geoms are horizontal or vertical.

### On analytical distributions: `stat_dist_[half]eye`

The same set of (half-)eye plot stats designed for sample data described above all have corresponding stats for analytical distributions: simply use `stat_dist_` instead of `stat_` in the name. These stats accept specifications for distributions using the `dist` and `args` aesthetics in one of two ways:

**Using distribution names as character vectors**: this format uses aesthetics as follows:

* `dist`: the name of the distribution, following R's naming scheme. This is a string which should have `"p"`, `"q"`, and `"d"` functions defined for it: e.g., "norm" is a valid distribution name because the `pnorm()`, `qnorm()`, and `dnorm()` functions define the CDF, quantile function, and density function of the Normal distribution.
* `args` or `arg1`, ... `arg9`: arguments for the distribution. If you use `args`, it should be a list column where each element is a list containing arguments for the distribution functions; alternatively, you can pass the arguments directly using `arg1`, ... `arg9`.

**Using distribution vectors from the [distributional](https://pkg.mitchelloharawild.com/distributional/) package**: this format uses aesthetics as follows:

* `dist`: a distribution vector produced by functions such as `distributional::dist_normal()`, `distributional::dist_beta()`, etc.

For example, here are a variety of normal distributions describing the same data from the previous example:

```{r dist_data}
dist_df = tribble(
    ~group, ~subgroup, ~mean, ~sd,
    "a",          "h",     5,   1,
    "b",          "h",     7,   1.5,
    "c",          "h",     8,   1,
    "c",          "i",     9,   1,
    "c",          "j",     7,   1
)
```

We can visualize these distributions directly using `stat_dist_eye()` and the character vector input style to the `dist`, `arg1`, and `arg2` aesthetics:

```{r dist_eye_dodge}
dist_df %>%
  ggplot(aes(x = group, dist = "norm", arg1 = mean, arg2 = sd, fill = subgroup)) +
  stat_dist_eye(position = "dodge") +
  ggtitle("stat_dist_eye(position = 'dodge')")
```

Or we can use the `distributional::dist_normal()` function to construct a vector of normal distributions. This syntax is often more compact and expressive than the character-vector format above:

```{r dist_eye_dodge_distributional}
dist_df %>%
  ggplot(aes(x = group, dist = dist_normal(mean, sd), fill = subgroup)) +
  stat_dist_eye(position = "dodge") +
  ggtitle("stat_dist_eye(position = 'dodge')")
```

This makes it easy to visualize a variety of distributions. E.g., here are some Beta distributions:

```{r beta_stacked}
data.frame(alpha = seq(5, 100, length.out = 10)) %>%
  ggplot(aes(y = alpha, dist = dist_beta(alpha, 10))) +
  stat_dist_halfeye() +
  labs(
    title = "stat_dist_halfeye()",
    x = "Beta(alpha,10) distribution"
  )
```

If you want to plot all of these on top of each other (instead of stacked), you could turn off plotting of the interval to make the plot easier to read using `stat_dist_halfeye(show_interval = FALSE, ...)`. A shortcut for `stat_dist_halfeye(show_interval = FALSE, ...)` is `stat_dist_slab()`. We'll also turn off the fill color with `fill = NA` to make the stacking easier to see, and use outline `color` to show the value of `alpha`:

```{r beta_overplotted_slabh}
data.frame(alpha = seq(5, 100, length.out = 10)) %>%
  ggplot(aes(y = "", dist = dist_beta(alpha, 10), color = alpha)) +
  stat_dist_slab(fill = NA) +
  coord_cartesian(expand = FALSE) +
  scale_color_viridis_c() +
  labs(
    title = "stat_dist_slab()",
    subtitle = "aes(dist = dist_beta(alpha, 10), color = alpha)",
    x = "Beta(alpha,10) distribution",
    y = NULL
  )
```

The approach of using `arg1`, ... `arg9` can work well when comparing similar distributions, but is harder to use with different distribution types. For example, if we wished to compare a Student t distribution and Normal distribution, the arguments may not line up. This is a good case to use list columns and the `args` aesthetic. `ggdist` includes an implementation of the scaled and shifted Student t distribution (`dstudent_t()`, `pstudent_t()`, etc) as it is often needed for visualizing frequentist confidence distributions (see `vignette("freq-uncertainty-vis")`) and Bayesian priors:

```{r norm_vs_t, fig.width = small_height, fig.height = small_height}
tribble(
  ~ dist,      ~ args,
  "norm",      list(0, 1),
  "student_t", list(3, 0, 1)
) %>%
  ggplot(aes(y = dist, dist = dist, args = args)) +
  stat_dist_halfeye() +
  ggtitle("stat_dist_halfeye()")
```

A particularly good use of the `dist` stats is to visualize priors. For example, with `brms` you can specify priors using the `brms::prior()` function, which creates data frames with a `"prior"` column indicating the name of the prior distribution as a string. E.g., I might set some priors on the betas and the standard deviation in a model with something like this:

```{r priors_fake, eval=FALSE}
# NB these priors are made up!
priors = c(
  prior(normal(0,1), class = b),
  prior(lognormal(0,1), class = sigma)
)
priors
```

```{r priors, echo=FALSE}
# we want to avoid a brms dependency, so we fake it above and
# just show the output of brms::prior() here
priors = data.frame(
  prior = c("normal(0, 1)", "lognormal(0, 1)"),
  class = c("b", "sigma"), coef = c("", ""),
  group = c("", ""),
  resp = c("", ""),
  dpar = c("", ""),
  nlpar = c("", ""),
  bound = c("", "")
)
priors
```

The `parse_dist` function can make it easier to visualize these: it takes in string specifications like those produced by `brms` --- `"normal(0,1)"` and `"lognormal(0,1)"` above --- and translates them into `.dist` and `.args` columns:

```{r parse_dist}
priors %>%
  parse_dist(prior)
```

Notice that it also automatically translate some common distribution names (e.g. "normal" and "lognormal") into their equivalent R function names (`"norm"` and `"lnorm"`). This makes it easy to use them with `stat_dist_eye()` and its variants:

```{r prior_dist_halfeyeh}
priors %>%
  parse_dist(prior) %>%
  ggplot(aes(y = class, dist = .dist, args = .args)) +
  stat_dist_halfeye() +
  labs(
    title = "stat_dist_halfeye()",
    subtitle = "with brms::prior() and ggdist::parse_dist() to visualize priors",
    x = NULL
  )
```

The `stat_dist_...` family also adjusts densities appropriately when scale transformations are applied. For example, here is a log-Normal distribution plotted on a log scale:

```{r dist_halfeyeh_log_scale, fig.width = small_height, fig.height = small_height}
data.frame(dist = "lnorm") %>%
  ggplot(aes(y = 0, dist = dist, arg1 = log(10), arg2 = 2*log(10))) +
  stat_dist_halfeye() +
  scale_x_log10(breaks = 10^seq(-5,7, by = 2))
```

As expected, a log-Normal density plotted on the log scale appears Normal. The Jacobian for the scale transformation is applied to the density so that the correct density is shown on the log scale. Internally, numerical differentiation is used to calculate the Jacobian so that the `stat_dist_...` family works generically across the different scale transformations supported by ggplot.

### Summing up eye plots: `stat_[dist_][half]eye`

All of the above geoms follow the naming scheme `stat_[dist_][half]eye`.

* Add `dist_` to the name to get stats for analytical distributions (otherwise it is for sample data).
* Add `half` to the name to get half-eyes (densities) instead of eyes (violins).

## Histogram + interval plots

In some cases you might prefer histograms to density plots. `stat_histinterval` provides an alternative to `stat_halfeye` that uses histograms instead of densities:

```{r stat_histinterval_horizontal, fig.width = med_width, fig.height = small_height}
p = df %>%
  ggplot(aes(x = group, y = value)) +
  panel_border()

ph = df %>%
  ggplot(aes(y = group, x = value)) +
  panel_border()

plot_grid(ncol = 2, align = "hv",
  p + stat_histinterval() + labs(title = "stat_histinterval()", subtitle = "horizontal"),
  ph + stat_histinterval() + labs(subtitle = "vertical")
)
```

You can use the `slab_color` aesthetic to show the outline of the bars. By default the outlines are only drawn on top of the bars, as typical tasks with histograms involve area estimation, so the outlines between bars are not strictly necessary and may be distracting. However, if you wish to include those outlines, you can set `outline_bars = TRUE`:

```{r stat_histintervalh_outlines, fig.width = med_width, fig.height = small_height}
plot_grid(ncol = 2, align = "hv",
  ph + stat_histinterval(slab_color = "gray45", outline_bars = FALSE) +
    labs(title = "stat_histinterval", subtitle = "outline_bars = FALSE (default)"),
  ph + stat_histinterval(slab_color = "gray45", outline_bars = TRUE) +
    labs(subtitle = "outline_bars = TRUE")
)
```

There are currently no analytical (`stat_dist_`) versions of `stat_histinterval()`.

## CCDF bar plots

Another (perhaps sorely underused) technique for visualizing distributions is cumulative distribution functions (CDFs) and complementary CDFs (CCDFs). These [can be more effective for some decision-making tasks](http://www.mjskay.com/papers/chi2018-uncertain-bus-decisions.pdf) than densities or intervals, and require fewer assumptions to create from sample data than density plots.

For all of the examples above, both on sample data and analytical distributions, you can replace `[half]eye` with `[c]cdfinterval` to get a stat that creates a CDF or CCDF bar plot. 

### On sample data: `stat_[c]cdfinterval`

`stat_[c]cdfinterval` has the following basic combinations:

```{r cdfinterval_family, fig.width = small_width, fig.height = small_width}
p = df %>%
  ggplot(aes(x = group, y = value)) +
  panel_border()

ph = df %>%
  ggplot(aes(y = group, x = value)) +
  panel_border()

plot_grid(ncol = 2, align = "hv",
  p + stat_ccdfinterval() + labs(title = "stat_ccdfinterval()", subtitle = "vertical"),
  ph + stat_ccdfinterval() + labs(subtitle = "horizontal"),
  p + stat_cdfinterval() + labs(title = "stat_cdfinterval()", subtitle = "vertical"),
  ph + stat_cdfinterval()  + labs(subtitle = "horizontal")
)
```

The CCDF interval plots are probably more useful than the CDF interval plots in most cases, as the bars typically grow up from the baseline. For example, replacing `stat_eye()` with `stat_ccdfinterval()` in our previous subgroup plot produces CCDF bar plots:

```{r ccdf_barplot}
df %>%
  ggplot(aes(x = group, y = value, fill = subgroup, group = subgroup)) +
  stat_ccdfinterval(position = "dodge") +
  ggtitle("stat_ccdfinterval(position = 'dodge')") 
```

The extents of the bars are determined automatically by range of the data in the samples. However, for bar charts it is often good practice to draw the bars from a meaningful reference point (this point is often 0). You can use `ggplot2::expand_limits()` to ensure the bar is drawn down to 0:

```{r ccdf_dodge}
df %>%
  ggplot(aes(x = group, y = value, fill = subgroup)) +
  stat_ccdfinterval(position = "dodge") +
  expand_limits(y = 0) +
  # plus coord_cartesian so there is no space between bars and axis
  coord_cartesian(expand = FALSE) +
  ggtitle("stat_ccdfinterval(position = 'dodge')")
```

You can also adjust the position of the slab relative to the position of the interval using the `justification` parameter:

```{r ccdf_justification}
df %>%
  ggplot(aes(x = group, y = value, fill = subgroup)) +
  stat_ccdfinterval(position = "dodge", justification = 1) +
  expand_limits(y = 0) +
  # clip = "off" needed here to ensure interval at the edge is visible
  coord_cartesian(expand = FALSE, clip = "off") +
  ggtitle("stat_ccdfinterval(position = 'dodge', justification = 1)")
```

The `side` parameter also works in the same way it does with `stat_eye()`. Here we'll demonstrate it horizontally:

```{r ccdf_side, fig.width = med_width, fig.height = tiny_height}
p = df %>%
  ggplot(aes(x = value, y = group)) +
  expand_limits(x = 0) +
  panel_border()

plot_grid(ncol = 3, align = "hv", 
  # side = "left" would give the same result
  p + stat_ccdfinterval(side = "bottom") + ggtitle("stat_ccdfinterval()") + labs(subtitle = "side = 'bottom'"),
  p + stat_ccdfinterval(side = "both") + labs(subtitle = "side = 'both'"),
  # side = "right" would give the same result
  p + stat_ccdfinterval(side = "top") + labs(subtitle = "side = 'top'")
)
```

### On analytical distributions: `stat_dist_[c]cdfinterval`

You can also use `stat_dist_ccdfinterval()` instead if you wish to visualize analytical distributions, just as you can use `stat_dist_eye()`.

By default, `stat_dist_ccdfinterval()` uses the quantiles at `p = 0.001` and `p = 0.999` of the distributions to determine their extent (unless the lower or upper limit of the distribution's support is finite, in which case that value is used). You can change this setting using the `p_limits` parameter, or use `expand_limits()` to ensure a particular value is shown, as before:

```{r dist_ccdf_dodge}
dist_df %>%
  ggplot(aes(x = group, dist = dist_normal(mean, sd), fill = subgroup)) +
  stat_dist_ccdfinterval(position = "dodge") +
  expand_limits(y = 0) +
  ggtitle("stat_dist_ccdfinterval(position = 'dodge')") +
  coord_cartesian(expand = FALSE)
```

### Summing up CDF bar plots: `stat_[dist_][c]cdfinterval`

All of the above geoms follow the naming scheme `stat_[dist_][c]cdfinterval`.

* Add `dist_` to the name to get stats for analytical distributions (otherwise it is for sample data).
* Add `c` to the name to get CCDFs instead of CDFs.

## Gradient plots

An alternative approach to mapping density onto the `thickness` aesthetic of the slab is to instead map it onto its `alpha` value (i.e., opacity). This is what the `stat_[dist_]gradientinterval` family does (actually, it uses `slab_alpha`, a variant of the `alpha` aesthetic, described below).

### On sample data: `stat_gradientinterval`

For example, replacing `stat_eye()` with `stat_gradientinterval()` produces gradient + interval plots:

```{r gradient_dodge}
df %>%
  ggplot(aes(x = group, y = value, fill = subgroup)) +
  stat_gradientinterval(position = "dodge") +
  labs(title = "stat_gradientinterval(position = 'dodge')")
```

`stat_gradientinterval()` maps density onto the `slab_alpha` aesthetic, which is a variant of the ggplot `alpha` scale that specifically targets alpha (opacity) values of the slab portion of `geom_slabinterval()`. This aesthetic has default ranges and limits that are a little different from the base ggplot `alpha` scale and which ensure that densities of 0 are mapped onto opacities of 0. You can use `scale_slab_alpha_continuous()` to adjust this scale's settings.

### On analytical distributions: `stat_dist_[c]cdfinterval`

As with other plot types, you can also use `stat_dist_gradientinterval()` instead if you wish to visualize analytical distributions:

```{r dist_gradient_dodge}
dist_df %>%
  ggplot(aes(x = group, dist = dist_normal(mean, sd), fill = subgroup)) +
  stat_dist_gradientinterval(position = "dodge") +
  labs(title = "stat_dist_gradientinterval(position = 'dodge')")
```

### Summing up gradient plots: `stat_[dist_]gradientinterval`

All of the above geoms follow the naming scheme `stat_[dist_]gradientinterval`.

* Add `dist_` to the name to get stats for analytical distributions (otherwise it is for sample data).
* Add `h` to the name to get the horizontal version.


## Dotplots

The encodings thus far are *continuous* probability encodings: they map probabilities or probability densities onto aesthetics like x/y position or transparency. An alternative is *discrete* or *frequency-framing* uncertainty visualizations, such as *dotplots* and *quantile dotplots*. These represent distributions as number of discrete possible outcomes.

### On sample data: `stat_dots`

For example, replacing `stat_halfeye()` with `stat_dots()` produces dotplots:

```{r dots_dodge, fig.width = med_width, fig.height = small_height}
df %>%
  ggplot(aes(x = group, y = value, fill = subgroup)) +
  stat_dots(position = "dodge") +
  labs(title = "stat_dots(position = 'dodge')")
```

Unlike the base `ggplot2::geom_dotplot()` geom, `ggdist::geom_dots()` automatically determines a bin width to ensure that the dot stacks fit within the available space. With so few dots here, the outlines mask the fill, so it makes sense to map the outline color of the dots as well:

```{r dots_dodge_nocolor, fig.width = med_width, fig.height = small_height}
df %>%
  ggplot(aes(x = group, y = value, fill = subgroup, color = subgroup)) +
  stat_dots(position = "dodge") +
  labs(title = "stat_dots(slab_color = NA)")
```

### Quantile dotplots

The above plots are a bit hard to read due to the large number of dots. Particularly when summarizing posterior distributions or predictive distributions, it can make sense to plot a smaller number of dots (say 20, 50 or 100) that are *representative* of the full sample. One such approach is to plot *quantiles*, thereby creating *quantile dotplots*, which can help people make decisions under uncertainty ([Kay 2016](https://doi.org/10.1145/2858036.2858558), [Fernandes 2018](https://doi.org/10.1145/3173574.3173718)).

The `quantiles` argument to `stat_dots` constructs a quantile dotplot with the specified number of quantiles. Here is one with 50 quantiles, so each dot represents approximately a 2% (1/50) chance. We'll turn off outline color too (`color = NA`):

```{r quantile_dots_dodge, fig.width = med_width, fig.height = small_height}
df %>%
  ggplot(aes(x = group, y = value, fill = subgroup)) +
  stat_dots(position = "dodge", quantiles = 50, color = NA) +
  labs(title = "stat_dots(quantiles = 50)")
```

### On analytical distributions: `stat_dist_dots`

As with other plot types, you can also use `stat_dist_dots()` instead if you wish to visualize analytical distributions. Analytical dotplots default to 100-dot quantile dotplots (as above, this can be adjusted with the `quantiles` argument). Shapes of the dots can also be changed using the `shape` aesthetic, and as with all slabinterval geoms, fill and color aesthetics can be varied within the geoms, as demonstrated below (we'll also put the group on the y axis to plot it horizontally):

```{r dist_dots_shape_color, fig.width = med_width, fig.height = large_height}
dist_df %>%
  ggplot(aes(y = group, dist = dist_normal(mean, sd), fill = stat(x < 5), shape = subgroup)) +
  stat_dist_dots(position = "dodge", color = NA) +
  labs(title = "stat_dist_dots(aes(fill = stat(x < 5), shape = subgroup))") +
  # we'll use these shapes since they retain outlines
  scale_shape_manual(values = c(21,22,23))
```

As with other slabinterval geoms, the `side` argument can also be used to construct violin-style dotplots. This example also shows the use of `dotsinterval` in place of `dots` to construct a combined quantile dotplot violin + interval plot. We also set `slab_color = NA` to turn off the outline on the dots:

```{r dist_dots_violin, fig.width = med_width, fig.height = small_height}
dist_df %>%
  ggplot(aes(x = group, dist = dist_normal(mean, sd), fill = subgroup)) +
  stat_dist_dotsinterval(position = "dodge", side = "both", slab_color = NA) +
  labs(title = "stat_dist_dotsinterval(side = 'both', slab_color = NA)") 
```

### Summing up dotplots: `stat_[dist_]dots[interval]`

All of the above geoms follow the naming scheme `stat_[dist_]dots[interval]`.

* Add `dist_` to the name to get stats for analytical distributions (otherwise it is for sample data).
* Add `interval` to the name to get the version with a point+interval geom overlaid.


## Custom plots

The `slabinterval` family of stats and geoms is designed to be very flexible. Most of the shortcut geoms above can be created simply by setting particular combinations of options and aesthetic mappings using the basic `geom_slabinterval()`, `stat_sample_slabinterval()`, and `stat_dist_slabinterval()`. Some useful combinations do not have specific shortcut geoms currently, but can be created manually with only a bit of additional effort.

### Gradients of alpha, color, and fill

Two aesthetics of particular use for creating custom geoms are `slab_alpha`, which changes the alpha transparency of the slab portion of the geom, `slab_color`, which changes its outline color, and `fill`, which changes its fill color. All of these aesthetics can be mapped to variables along the length of the geom (that is, the color does not have to be constant over the entire geom), which allows you to create gradients or to highlight meaningful regions of the data (amongst other things). You can also employ the ggdist-specific `color_ramp` and `fill_ramp`
aesthetics to create custom gradients with outline and fill colors, as demonstrated later in this section.

### CCDF Gradients

For example, `stat_ccdfinterval()` maps the output of the evaluated function (in its case, the CCDF) onto the `thickness` aesthetic of the `slabinterval` geom, which determines how thick the slab is. This is the equivalent of setting `aes(thickness = stat(f))`. However, we could instead create a CCDF gradient plot, a sort of mashup of a CCDF barplot and a density gradient plot, by mapping `stat(f)` onto the `slab_alpha` aesthetic instead, and setting `thickness` to a constant (1):

```{r ccdf_gradient, fig.width = med_width, fig.height = small_height}
df %>%
  ggplot(aes(x = group, y = value, fill = subgroup)) +
  stat_ccdfinterval(aes(slab_alpha = stat(f)), thickness = 1, position = "dodge") +
  expand_limits(y = 0) +
  # plus coord_cartesian so there is no space between bars and axis
  coord_cartesian(expand = FALSE) +
  ggtitle("stat_ccdfinterval(aes(slab_alpha = stat(f)), thickness = 1)")
```

If this approach were applied to bins in a histogram, where each bin had some uncertainty
associated with its height, the result would be a so-called *fuzzygram* ([Wilkinson 1992](https://doi.org/10.1177/096228029200100102)).

### Highlighting and other combinations

The ability to map arbitrary variables onto fill or outline colors within a slab allows you to easily highlight sub-regions of a plot. Take the earlier example of visualizing priors:

```{r norm_vs_t_2, fig.width = small_width, fig.height = small_height}
priors = tribble(
  ~ dist,      ~ args,
  "norm",      list(0, 1),
  "student_t", list(3, 0, 1)
) 

priors %>%
  ggplot(aes(y = dist, dist = dist, args = args)) +
  stat_dist_halfeye() +
  ggtitle("stat_dist_halfeye()")
```

We can add a mapping to the `fill` aesthetic to highlight a region of interest, say ±1.5:

```{r norm_vs_t_highlight, fig.width = med_width, fig.height = small_height}
priors %>%
  ggplot(aes(y = dist, dist = dist, args = args)) +
  stat_dist_halfeye(aes(fill = stat(abs(x) < 1.5))) +
  ggtitle("stat_dist_halfeye(aes(fill = stat(abs(x) < 1.5)))") +
  # we'll use a nicer palette than the default for highlighting:
  scale_fill_manual(values = c("gray85", "skyblue"))
```

We could also combine these aesthetics arbitrarily. Here is a (probably not very useful) eye plot + gradient plot combination, with the portion of the distribution above 1 highlighted:

```{r norm_vs_t_gradient_eye, fig.width = med_width, fig.height = small_height}
priors %>%
  ggplot(aes(y = dist, dist = dist, args = args)) +
  stat_dist_eye(aes(slab_alpha = stat(f), fill = stat(x > 1))) +
  ggtitle("stat_dist_eye(aes(slab_alpha = stat(f), fill = stat(x > 1)))") +
  # we'll use a nicer palette than the default for highlighting:
  scale_fill_manual(values = c("gray75", "skyblue"))
```

### Mashups with Correll and Gleicher-style gradients

We can also take advantage of the fact that all slabinterval stats also supply `cdf` and `pdf` aesthetics to create charts make use of both the CDF and the PDF in their aesthetic mappings. For example, we could create [Correll & Gleicher](https://doi.org/10.1109/TVCG.2014.2346298)-style gradient plots by fading the tails outside of the 95% interval in proportion to $|1 - 2F(x)|$ (where $F(x)$ is the CDF):

```{r correll_gradient, fig.width = med_width, fig.height = small_height/2}
priors %>%
  ggplot(aes(y = dist, dist = dist, args = args)) +
  stat_dist_gradientinterval(aes(slab_alpha = stat(-pmax(abs(1 - 2*cdf), .95)))) +
  scale_slab_alpha_continuous(guide = FALSE)
```

We could also do a mashup of faded-tail gradients with violin plots by starting with an eye plot and then using the generated `cdf` aesthetic to fade the tails, producing plots like those in [Helske *et al.*](https://arxiv.org/abs/2002.07671):

```{r helske_gradient_eye, fig.width = med_width, fig.height = small_height}
priors %>%
  ggplot(aes(y = dist, dist = dist, args = args)) +
  stat_dist_eye(aes(slab_alpha = stat(-pmax(abs(1 - 2*cdf), .95)))) +
  scale_slab_alpha_continuous(guide = FALSE)
```

### Densities filled according to intervals

Another common chart type involves filling in the interior of a halfeye plot
according to some intervals. We can again use the fact that slabinterval stats
auto-calculate both the PDF and CDF of a distribution as statistics. We can then
the `cut_cdf_qi()` function, which labels points in a CDF according to
which quantile interval they fall into, to determine the fill color:

```{r halfeye_filled_intervals, fig.width = med_width, fig.height = small_height}
df %>%
  ggplot(aes(y = group, x = value)) +
  stat_halfeye(aes(fill = stat(cut_cdf_qi(cdf)))) +
  scale_fill_brewer(direction = -1) +
  labs(
    title = "stat_halfeye()", 
    subtitle = "aes(fill = stat(cut_cdf_qi(cdf)))",
    fill = "Interval"
  )
```

Like `point_interval()`, `cut_cdf_qi()` takes a `.width` parameter to define the intervals,
with a default of `c(.66, .95, 1)`. The final `1` is necessary to show the full
density, to cut off the tails of the density you can omit it.
Like ggplot scales, `cut_cdf_qi()` also takes a `labels` parameter to define the labels of
the intervals (or to provide a function to define the labels, such as a
formatting function like `scales::percent_format()`). Let's modify the intervals to 
show the 50%, 80%, and 95% intervals, omitting the tails of the density and
reformatting the interval labels to use percentages. We can also use
`na.translate = FALSE` to drop the unnecessary `NA` level from the fill scale:

```{r halfeye_filled_intervals_2, fig.width = med_width, fig.height = small_height}
df %>%
  ggplot(aes(y = group, x = value)) +
  stat_halfeye(aes(fill = stat(cut_cdf_qi(
    cdf, 
    .width = c(.5, .8, .95),
    labels = scales::percent_format()
  )))) +
  scale_fill_brewer(direction = -1, na.translate = FALSE) +
  labs(
    title = "stat_halfeye()", 
    subtitle = "aes(fill = stat(cut_cdf_qi(cdf, .width = c(.5, .8, .95))))",
    fill = "Interval"
  )
```

### Using color ramps for `fill` and `color` aesthetics

`ggdist` supplies `color_ramp` (or `colour_ramp`) and `fill_ramp` aesthetics
which can be used to vary ("ramp") the outline or fill colors smoothly from a 
base color (default `"white"`) to whatever color the geometry would otherwise 
have.

Taking the above example with `cut_cdf_qi()`, we could use the `fill_ramp` aesthetic
instead of the `fill` aesthetic to set the slab color based on the interval it is in.
We could then vary the base fill color separately from the interval based on 
another column in the original data table, such as the `subgroup` column:

```{r halfeye_filled_intervals_subgroup, fig.width = med_width, fig.height = small_height}
df %>%
  ggplot(aes(y = group, x = value)) +
  stat_halfeye(
    aes(
      fill = subgroup,
      fill_ramp = stat(cut_cdf_qi(
        cdf, 
        .width = c(.5, .8, .95),
        labels = scales::percent_format()
      ))
    ),
    position = "dodge",
  ) +
  # a range from 1 down to 0.2 ensures the fill goes dark to light inside-out
  # and doesn't get all the way down to white (0) on the lightest color
  scale_fill_ramp_discrete(range = c(1, 0.2), na.translate = FALSE) +
  labs(
    title = "stat_halfeye()", 
    subtitle = "aes(fill = subgroup, fill_ramp = stat(cut_cdf_qi(cdf)))",
    fill_ramp = "Interval"
  )
```

We could similarly use the `stat_dist_interval()` (or `stat_interval()`) geometries
with the `color_ramp` aesthetic to vary subgroup color separately from the
whiteness of the intervals. Here, `level` is a variable generated by all stats in
the `stat_dist_...` family which contains the level of the generated intervals,
as an ordered factor.

```{r dist_interval_color_ramp, fig.width = med_width, fig.height = small_height}
dist_df %>%
  ggplot(aes(x = group, dist = dist_normal(mean, sd), color = subgroup)) +
  stat_dist_interval(aes(color_ramp = stat(level)), position = "dodge") +
  labs(
    title = "stat_dist_interval()", 
    subtitle = "aes(color = subgroup, color_ramp = stat(level))"
  )
```

See `help("scale_color_ramp")` for more information on the color ramp aesthetics/scales.

### Independent slabs and intervals in composite plots

Sometimes when constructing composite plots it may be useful to position slab and interval parts of the geometry separately.
While some relative positioning of these geometries is supported by manipulating the `justification` parameter, if you
want complete, separate control over positioning of intervals versus slabs, the simplest approach can be to specify those
geometries separately. 

For example, the following uses a separate specification of a `stat_slab()` and a `stat_pointinterval()` instead of a combined `stat_slabinterval()` in order to use `position_dodge()` on the intervals but not the slabs:

```{r slab_and_pointinterval, fig.width = med_width, fig.height = small_height}
df %>%
  ggplot(aes(fill = group, color = group, x = value)) +
  stat_slab(alpha = .3) +
  stat_pointinterval(position = position_dodge(width = .4, preserve = "single")) +
  labs(
    title = "stat_slab() and stat_pointinterval()", 
    subtitle = "with position_dodge() applied to the intervals",
    y = NULL
  ) +
  scale_y_continuous(breaks = NULL)
```

(Thanks to Brenton Wiernik for [this example](https://github.com/mjskay/ggdist/issues/27#issuecomment-725578437).)


```{r reset_options, include=FALSE}
options(.old_options)
```
