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% Please edit documentation in R/hdi.R
\title{Highest Density Interval (HDI)}
hdi(x, ...)

\method{hdi}{numeric}(x, ci = 0.89, verbose = TRUE, ...)

\method{hdi}{data.frame}(x, ci = 0.89, verbose = TRUE, ...)

\method{hdi}{stanreg}(x, ci = 0.89, effects = c("fixed", "random",
  "all"), parameters = NULL, verbose = TRUE, ...)

\method{hdi}{brmsfit}(x, ci = 0.89, effects = c("fixed", "random",
  "all"), component = c("conditional", "zi", "zero_inflated", "all"),
  parameters = NULL, verbose = TRUE, ...)

\method{hdi}{BFBayesFactor}(x, ci = 0.89, verbose = TRUE, ...)
\item{x}{Vector representing a posterior distribution. Can also be a
\code{stanreg} or \code{brmsfit} model.}

\item{...}{Currently not used.}

\item{ci}{Value or vector of probability of the interval (between 0 and 1)
to be estimated. Named Credible Interval (CI) for consistency.}

\item{verbose}{Toggle off warnings.}

\item{effects}{Should results for fixed effects, random effects or both be returned?
Only applies to mixed models. May be abbreviated.}

\item{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.}

\item{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.}
A data frame with following columns:
    \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.
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)}.
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 89\% intervals (\code{ci = 0.89}),
  deemed to be more stable than, for instance, 95\% intervals (\cite{Kruschke, 2014}).
  An effective sample size of at least 10.000 is recommended if 95\% intervals
  should be computed (\cite{Kruschke, 2014, p. 183ff}). Moreover, 89 is the
  highest prime number that does not exceed the already unstable 95\% threshold.
  What does it have to do with anything? Nothing, but it reminds us of the total
  arbitrarity of any of these conventions (McElreath, 2015).

posterior <- rnorm(1000)
hdi(posterior, ci = .89)
hdi(posterior, ci = c(.80, .90, .95))

df <- data.frame(replicate(4, rnorm(100)))
hdi(df, ci = c(.80, .90, .95))

model <- stan_glm(mpg ~ wt + gear, data = mtcars, chains = 2, iter = 200)
hdi(model, ci = c(.80, .90, .95))

model <- brms::brm(mpg ~ wt + cyl, data = mtcars)
hdi(model, ci = c(.80, .90, .95))

bf <- ttestBF(x = rnorm(100, 1, 1))
hdi(bf, ci = c(.80, .90, .95))

  \item Kruschke, J. (2014). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press.
  \item McElreath, R. (2015). Statistical rethinking: A Bayesian course with examples in R and Stan. Chapman and Hall/CRC.
Credits go to \href{https://rdrr.io/cran/ggdistribute/src/R/stats.R}{ggdistribute} and \href{https://github.com/mikemeredith/HDInterval}{HDInterval}.
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