Scatterplot colored by highest density regions of a bivariate pdf

Compute the highest density regions (HDRs) of a bivariate pdf and plot the provided data as a scatterplot with points colored according to their corresponding HDR.

Usage

stat_hdr_points_fun(
  mapping = NULL,
  data = NULL,
  geom = "point",
  position = "identity",
  ...,
  fun,
  args = list(),
  probs = c(0.99, 0.95, 0.8, 0.5),
  xlim = NULL,
  ylim = NULL,
  n = 100,
  na.rm = FALSE,
  show.legend = NA,
  inherit.aes = TRUE
)

geom_hdr_points_fun(
  mapping = NULL,
  data = NULL,
  stat = "hdr_points_fun",
  position = "identity",
  ...,
  na.rm = FALSE,
  show.legend = NA,
  inherit.aes = TRUE
)

Arguments

mapping

Set of aesthetic mappings created by aes(). If specified and inherit.aes = TRUE (the default), it is combined with the default mapping at the top level of the plot. You must supply mapping if there is no plot mapping.

data

The data to be displayed in this layer. There are three options:

If NULL, the default, the data is inherited from the plot data as specified in the call to ggplot().

A data.frame, or other object, will override the plot data. All objects will be fortified to produce a data frame. See fortify() for which variables will be created.

A function will be called with a single argument, the plot data. The return value must be a data.frame, and will be used as the layer data. A function can be created from a formula (e.g. ~ head(.x, 10)).

geom

The geometric object to use to display the data, either as a ggproto Geom subclass or as a string naming the geom stripped of the geom_ prefix (e.g. "point" rather than "geom_point")

position

Position adjustment, either as a string naming the adjustment (e.g. "jitter" to use position_jitter), or the result of a call to a position adjustment function. Use the latter if you need to change the settings of the adjustment.

...

Other arguments passed on to layer(). These are often aesthetics, used to set an aesthetic to a fixed value, like colour = "red" or size = 3. They may also be parameters to the paired geom/stat.

fun

A function, the joint probability density function, must be vectorized in its first two arguments; see examples.

args

Named list of additional arguments passed on to fun.

probs

Probabilities to compute highest density regions for.

xlim, ylim

Range to compute and draw regions. If NULL, defaults to range of data if present.

n

Number of grid points in each direction.

na.rm

If FALSE, the default, missing values are removed with a warning. If TRUE, missing values are silently removed.

show.legend

logical. Should this layer be included in the legends? NA, the default, includes if any aesthetics are mapped. FALSE never includes, and TRUE always includes. It can also be a named logical vector to finely select the aesthetics to display.

inherit.aes

If FALSE, overrides the default aesthetics, rather than combining with them. This is most useful for helper functions that define both data and aesthetics and shouldn't inherit behaviour from the default plot specification, e.g. borders().

stat

The statistical transformation to use on the data for this layer, either as a ggproto Geom subclass or as a string naming the stat stripped of the stat_ prefix (e.g. "count" rather than "stat_count")

Aesthetics

geom_hdr_points_fun understands the following aesthetics (required aesthetics are in bold):

• x

• y

• alpha

• color

• fill

• group

• linetype

• size

• subgroup

Computed variables

probs

The probability associated with the highest density region, specified by probs.

Examples

# Can plot points colored according to known pdf:
set.seed(1)
df <- data.frame(x = rexp(1000), y = rexp(1000))
f <- function(x, y) dexp(x) * dexp(y)

ggplot(df, aes(x, y)) +
  geom_hdr_points_fun(fun = f, xlim = c(0, 10), ylim = c(0, 10))



# Also allows for hdrs of a custom parametric model

# generate example data
n <- 1000
th_true <- c(3, 8)

rdata <- function(n, th) {
  gen_single_obs <- function(th) {
    rchisq(2, df = th) # can be anything
  }
  df <- replicate(n, gen_single_obs(th))
  setNames(as.data.frame(t(df)), c("x", "y"))
}
data <- rdata(n, th_true)

# estimate unknown parameters via maximum likelihood
likelihood <- function(th) {
  th <- abs(th) # hack to enforce parameter space boundary
  log_f <- function(v) {
    x <- v[1]; y <- v[2]
    dchisq(x, df = th[1], log = TRUE) + dchisq(y, df = th[2], log = TRUE)
  }
  sum(apply(data, 1, log_f))
}
(th_hat <- optim(c(1, 1), likelihood, control = list(fnscale = -1))$par)
#> [1] 3.059391 8.084245

# plot f for the give model
f <- function(x, y, th) dchisq(x, df = th[1]) * dchisq(y, df = th[2])

ggplot(data, aes(x, y)) +
  geom_hdr_points_fun(fun = f, args = list(th = th_hat))


ggplot(data, aes(x, y)) +
  geom_hdr_points_fun(aes(fill = after_stat(probs)), shape = 21, color = "black",
    fun = f, args = list(th = th_hat), na.rm = TRUE) +
  geom_hdr_lines_fun(aes(color = after_stat(probs)), alpha = 1, fun = f, args = list(th = th_hat)) +
  lims(x = c(0, 15), y = c(0, 25))