Highest Density Region (HDR) plots

If f(x) is the density function of a random variable X, then the 100 (1−α) HDR is the subset R(fα) of the sample space of X such that R(fα)={x:f(x)≥fα}, where fα is the largest constant such that Pr(X∈R(fα))≥1−α).

Graphing HDRs using R package hdrcde

Data set: Waiting time between eruptions and the duration of the eruption for the Old Faithful geyser in Yellowstone National Park, Wyoming, USA.

faithful %>% as_tibble

## # A tibble: 272 x 2
##    eruptions waiting
##        <dbl>   <dbl>
##  1      3.6       79
##  2      1.8       54
##  3      3.33      74
##  4      2.28      62
##  5      4.53      85
##  6      2.88      55
##  7      4.7       88
##  8      3.6       85
##  9      1.95      51
## 10      4.35      85
## # … with 262 more rows

Graphing HDRs using R package hdrcde

Extending ggplot2

• HDR is a novel technique for summarizing distribution for which plotting is not implemented in ggplot2
• ggplot2 creates graphics based on The Grammar of Graphics
• graphics are built step by step by adding new elements that allows for extensive flexibility and customization of plots
• need to extend the functionality of ggplot2

HDR boxplots

library(hdrcde)
hdr.boxplot(faithful$eruptions)

library(gghdr)
library(ggplot2)
ggplot(faithful, aes(y = eruptions)) +
  geom_hdr_boxplot()

HDR rug plots and scatter plots

faithful %>% 
  ggplot(aes(x = waiting, 
             y = eruptions)) + 
  geom_hdr_rug(fill = "blue") + 
  geom_point()

faithful %>%
  ggplot(aes(x = waiting,
             y = eruptions)) +  
  geom_point(aes(colour =  
  hdr_bin(x = waiting,y = eruptions)))

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