hdi.R
#' Highest Density Interval (HDI)
#'
#' Compute the \strong{Highest Density Interval (HDI)} of a posterior distribution, i.e., all points within the interval have a higher probability density than points outside the interval. The HDI can be used in the context of Bayesian posterior characterisation as \strong{Credible Interval (CI)}.
#'
#' @details Unlike equal-tailed intervals (see \link{ci}) that typically exclude 2.5\% from each tail
#' of the distribution, the HDI is \emph{not} equal-tailed and therefore always
#' includes the mode(s) of posterior distributions.
#' \cr \cr
#' By default, \code{hdi()} returns the 90\% intervals (\code{ci = 0.9}),
#' deemed to be more stable than, for instance, 95\% intervals (\cite{Kruschke, 2015}).
#' An effective sample size of at least 10.000 is recommended if 95\% intervals
#' should be computed (\cite{Kruschke, 2015, p. 183ff}).
#'
#' @param x Vector representing a posterior distribution. Can also be a
#' \code{stanreg} or \code{brmsfit} model.
#' @param ci Value or vector of probability of the interval (between 0 and 1)
#' to be estimated. Named Credible Interval (CI) for consistency.
#' @param effects Should results for fixed effects, random effects or both be returned?
#' Only applies to mixed models. May be abbreviated.
#' @param component Should results for all parameters, parameters for the conditional model
#' or the zero-inflated part of the model be returned? May be abbreviated. Only
#' applies to \pkg{brms}-models.
#' @param parameters Regular expression pattern that describes the parameters that
#' should be returned. Meta-parameters (like \code{lp__} or \code{prior_}) are
#' filtered by default, so only parameters that typically appear in the
#' \code{summary()} are returned. Use \code{parameters} to select specific parameters
#' for the output.
#' @param verbose Toggle off warnings.
#' @param ... Currently not used.
#'
#' @return A data frame with following columns:
#' \itemize{
#' \item \code{Parameter} The model parameter(s), if \code{x} is a model-object. If \code{x} is a vector, this column is missing.
#' \item \code{CI} The probability of the HDI.
#' \item \code{CI_low} , \code{CI_high} The lower and upper HDI limits for the parameters.
#' }
#'
#' @examples
#' library(bayestestR)
#'
#' posterior <- rnorm(1000)
#' hdi(posterior, ci = .90)
#' hdi(posterior, ci = c(.80, .90, .95))
#' \dontrun{
#' library(rstanarm)
#' model <- rstanarm::stan_glm(mpg ~ wt + cyl, data = mtcars)
#' hdi(model)
#' hdi(model, ci = c(.80, .90, .95))
#'
#' library(brms)
#' model <- brms::brm(mpg ~ wt + cyl, data = mtcars)
#' hdi(model)
#' hdi(model, ci = c(.80, .90, .95))
#' }
#'
#' @author Credits go to \href{https://rdrr.io/cran/ggdistribute/src/R/stats.R}{ggdistribute} and \href{https://github.com/mikemeredith/HDInterval}{HDInterval}.
#'
#' @references Kruschke, J. (2015). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press.
#'
#' @export
hdi <- function(x, ...) {
UseMethod("hdi")
}
#' @rdname hdi
#' @export
hdi.numeric <- function(x, ci = .90, verbose = TRUE, ...) {
do.call(rbind, lapply(ci, function(i) {
.hdi(x, ci = i, verbose = verbose)
}))
}
#' @importFrom insight get_parameters
#' @rdname hdi
#' @export
hdi.stanreg <- function(x, ci = .90, effects = c("fixed", "random", "all"), parameters = NULL, verbose = TRUE, ...) {
effects <- match.arg(effects)
.compute_interval_stanreg(x, ci, effects, parameters, verbose, fun = "hdi")
}
#' @rdname hdi
#' @export
hdi.brmsfit <- function(x, ci = .90, effects = c("fixed", "random", "all"), component = c("conditional", "zi", "zero_inflated", "all"), parameters = NULL, verbose = TRUE, ...) {
effects <- match.arg(effects)
component <- match.arg(component)
.compute_interval_brmsfit(x, ci, effects, component, parameters, verbose, fun = "hdi")
}
#' @keywords internal
.hdi <- function(x, ci = .90, verbose = TRUE) {
check_ci <- .check_ci_argument(x, ci, verbose)
if (!is.null(check_ci)) {
return(check_ci)
}
x_sorted <- sort.int(x, method = "quick") # removes NA/NaN, but not Inf
window_size <- ceiling(ci * length(x_sorted)) # See https://github.com/easystats/bayestestR/issues/39
if (window_size < 2) {
if (verbose) {
warning("`ci` is too small or x does not contain enough data points, returning NAs.")
}
return(data.frame(
"CI" = ci * 100,
"CI_low" = NA,
"CI_high" = NA
))
}
nCIs <- length(x_sorted) - window_size
ci.width <- sapply(1:nCIs, function(.x) x_sorted[.x + window_size] - x_sorted[.x])
# find minimum of width differences, check for multiple minima
min_i <- which(ci.width == min(ci.width))
n_candies <- length(min_i)
if (n_candies > 1) {
if (any(diff(sort(min_i)) != 1)) {
if (verbose) {
warning("Identical densities found along different segments of the distribution, choosing rightmost.")
}
min_i <- max(min_i)
} else {
min_i <- floor(mean(min_i))
}
}
data.frame(
"CI" = ci * 100,
"CI_low" = x_sorted[min_i],
"CI_high" = x_sorted[min_i + window_size]
)
}