R/curve_interval.R
curve_interval.Rd
Translates draws from distributions in a grouped data frame into a set of point and interval summaries using a curve boxplotinspired approach.
curve_interval( .data, ..., .along = NULL, .width = 0.5, .interval = c("mhd", "mbd", "bd", "bdmbd"), .simple_names = TRUE, na.rm = FALSE, .exclude = c(".chain", ".iteration", ".draw", ".row") )
.data  Data frame (or grouped data frame as returned by 

...  Bare column names or expressions that, when evaluated in the context of

.along  Which columns are the input values to the function describing the curve (e.g., the "x"
values). Supports tidyselect syntax, as in 
.width  vector of probabilities to use that determine the widths of the resulting intervals.
If multiple probabilities are provided, multiple rows per group are generated, each with
a different probability interval (and value of the corresponding 
.interval  The method used to calculate the intervals. Currently, all methods rank the curves
using some measure of data depth, then create envelopes containing the

.simple_names  When 
na.rm  logical value indicating whether 
.exclude  A character vector of names of columns to be excluded from summarization if no column names are specified to be summarized. Default ignores several metadata column names used in tidybayes. 
A data frame containing point summaries and intervals, with at least one column corresponding
to the point summary, one to the lower end of the interval, one to the upper end of the interval, the
width of the interval (.width
), the type of point summary (.point
), and the type of interval (.interval
).
Intervals are calculated by ranking the curves using some measure of data depth, then
using binary search to find a cutoff k
such that an envelope containing the k
% "deepest"
curves also contains .width
% of the curves, for each value of .width
(note that k
and .width
are not necessarily the same). This is in contrast to most functional boxplot
or curve boxplot approaches, which tend to simply take the .width
% deepest curves, and
are generally quite conservative (i.e. they may contain more than .width
% of the curves).
See Mirzargar et al. (2014) or Juul et al. (2020) for an accessible introduction to data depth and curve boxplots / functional boxplots.
Fraiman, Ricardo and Graciela Muniz. (2001). "Trimmed means for functional data". Test 10: 419–440. doi: 10.1007/BF02595706 .
Sun, Ying and Marc G. Genton. (2011). "Functional Boxplots". Journal of Computational and Graphical Statistics, 20(2): 316334. doi: 10.1198/jcgs.2011.09224
Mirzargar, Mahsa, Ross T Whitaker, and Robert M Kirby. (2014). "Curve Boxplot: Generalization of Boxplot for Ensembles of Curves". IEEE Transactions on Visualization and Computer Graphics. 20(12): 26542663. doi: 10.1109/TVCG.2014.2346455
Juul Jonas, Kaare Græsbøll, Lasse Engbo Christiansen, and Sune Lehmann. (2020). "Fixedtime descriptive statistics underestimate extremes of epidemic curve ensembles". arXiv eprint. arXiv:2007.05035
point_interval()
for pointwise intervals. See vignette("lineribbon")
for more examples
and discussion of the differences between pointwise and curvewise intervals.
Matthew Kay
library(dplyr) library(ggplot2) # generate a set of curves k = 11 # number of curves n = 201 df = tibble( .draw = rep(1:k, n), mean = rep(seq(5,5, length.out = k), n), x = rep(seq(15,15,length.out = n), each = k), y = dnorm(x, mean, 3) ) # see pointwise intervals... df %>% group_by(x) %>% median_qi(y, .width = c(.5)) %>% ggplot(aes(x = x, y = y)) + geom_lineribbon(aes(ymin = .lower, ymax = .upper)) + geom_line(aes(group = .draw), alpha=0.15, data = df) + scale_fill_brewer() + ggtitle("50% pointwise intervals with point_interval()") + theme_ggdist() # ... compare them to curvewise intervals if (requireNamespace("posterior", quietly = TRUE)) { df %>% group_by(x) %>% curve_interval(y, .width = c(.5)) %>% ggplot(aes(x = x, y = y)) + geom_lineribbon(aes(ymin = .lower, ymax = .upper)) + geom_line(aes(group = .draw), alpha=0.15, data = df) + scale_fill_brewer() + ggtitle("50% curvewise intervals with curve_interval()") + theme_ggdist() }