#' Bias Corrected and Accelerated Interval (BCa)
#'
#' Compute the \strong{Bias Corrected and Accelerated Interval (BCa)} of posterior distributions.
#'
#' @inheritParams hdi
#' @inherit ci return
#' @inherit hdi details
#'
#' @references DiCiccio, T. J. and B. Efron. (1996). Bootstrap Confidence Intervals. Statistical Science. 11(3): 189–212. \doi{10.1214/ss/1032280214}
#'
#' @examples
#' posterior <- rnorm(1000)
#' bci(posterior)
#' bci(posterior, ci = c(.80, .89, .95))
#' @export
bci <- function(x, ...) {
  UseMethod("bci")
}

#' @rdname bci
#' @export
bcai <- bci



#' @rdname bci
#' @export
bci.numeric <- function(x, ci = 0.95, verbose = TRUE, ...) {
  out <- do.call(rbind, lapply(ci, function(i) {
    .bci(x = x, ci = i, verbose = verbose)
  }))
  class(out) <- unique(c("bayestestR_eti", "see_eti", "bayestestR_ci", "see_ci", class(out)))
  attr(out, "data") <- x
  out
}



#' @rdname bci
#' @export
bci.data.frame <- function(x, ci = 0.95, verbose = TRUE, ...) {
  dat <- .compute_interval_dataframe(x = x, ci = ci, verbose = verbose, fun = "bci")
  attr(dat, "object_name") <- .safe_deparse(substitute(x))
  dat
}



#' @rdname bci
#' @export
bci.MCMCglmm <- function(x, ci = 0.95, verbose = TRUE, ...) {
  nF <- x$Fixed$nfl
  d <- as.data.frame(x$Sol[, 1:nF, drop = FALSE])
  dat <- .compute_interval_dataframe(x = d, ci = ci, verbose = verbose, fun = "bci")
  attr(dat, "data") <- .safe_deparse(substitute(x))
  dat
}



#' @export
bci.mcmc <- function(x, ci = 0.95, verbose = TRUE, ...) {
  d <- as.data.frame(x)
  dat <- .compute_interval_dataframe(x = d, ci = ci, verbose = verbose, fun = "bci")
  attr(dat, "data") <- .safe_deparse(substitute(x))
  dat
}



#' @export
bci.bamlss <- function(x, ci = 0.95, component = c("all", "conditional", "location"), verbose = TRUE, ...) {
  component <- match.arg(component)
  d <- insight::get_parameters(x, component = component)
  dat <- .compute_interval_dataframe(x = d, ci = ci, verbose = verbose, fun = "bci")
  attr(dat, "data") <- .safe_deparse(substitute(x))
  dat
}



#' @export
bci.bcplm <- function(x, ci = 0.95, verbose = TRUE, ...) {
  d <- insight::get_parameters(x)
  dat <- .compute_interval_dataframe(x = d, ci = ci, verbose = verbose, fun = "bci")
  attr(dat, "data") <- .safe_deparse(substitute(x))
  dat
}


#' @export
bci.bayesQR <- bci.bcplm

#' @export
bci.blrm <- bci.bcplm

#' @export
bci.mcmc.list <- bci.bcplm

#' @export
bci.BGGM <- bci.bcplm



#' @rdname bci
#' @export
bci.sim.merMod <- function(x, ci = 0.95, effects = c("fixed", "random", "all"), parameters = NULL, verbose = TRUE, ...) {
  effects <- match.arg(effects)
  dat <- .compute_interval_simMerMod(x = x, ci = ci, effects = effects, parameters = parameters, verbose = verbose, fun = "bci")
  out <- dat$result
  attr(out, "data") <- dat$data
  out
}



#' @rdname bci
#' @export
bci.sim <- function(x, ci = 0.95, parameters = NULL, verbose = TRUE, ...) {
  dat <- .compute_interval_sim(x = x, ci = ci, parameters = parameters, verbose = verbose, fun = "bci")
  out <- dat$result
  attr(out, "data") <- dat$data
  out
}



#' @rdname bci
#' @export
bci.emmGrid <- function(x, ci = 0.95, verbose = TRUE, ...) {
  xdf <- insight::get_parameters(x)

  dat <- eti(xdf, ci = ci, verbose = verbose, ...)
  attr(dat, "object_name") <- .safe_deparse(substitute(x))
  dat
}

#' @export
bci.emm_list <- bci.emmGrid

#' @rdname bci
#' @export
bci.stanreg <- function(x, ci = 0.95, effects = c("fixed", "random", "all"),
                        component = c("location", "all", "conditional", "smooth_terms", "sigma", "distributional", "auxiliary"),
                        parameters = NULL, verbose = TRUE, ...) {
  effects <- match.arg(effects)
  component <- match.arg(component)

  out <- .prepare_output(
    eti(insight::get_parameters(x, effects = effects, component = component, parameters = parameters), ci = ci, verbose = verbose, ...),
    insight::clean_parameters(x),
    inherits(x, "stanmvreg")
  )

  class(out) <- unique(c("bayestestR_eti", "see_eti", class(out)))
  attr(out, "object_name") <- .safe_deparse(substitute(x))
  out
}


#' @export
bci.stanfit <- bci.stanreg

#' @export
bci.blavaan <- bci.stanreg



#' @rdname bci
#' @export
bci.brmsfit <- function(x, ci = 0.95, effects = c("fixed", "random", "all"),
                        component = c("conditional", "zi", "zero_inflated", "all"),
                        parameters = NULL, verbose = TRUE, ...) {
  effects <- match.arg(effects)
  component <- match.arg(component)

  out <- .prepare_output(
    eti(insight::get_parameters(x, effects = effects, component = component, parameters = parameters), ci = ci, verbose = verbose, ...),
    insight::clean_parameters(x)
  )

  class(out) <- unique(c("bayestestR_eti", "see_eti", class(out)))
  attr(out, "object_name") <- .safe_deparse(substitute(x))
  out
}



#' @rdname bci
#' @export
bci.BFBayesFactor <- function(x, ci = 0.95, verbose = TRUE, ...) {
  out <- eti(insight::get_parameters(x), ci = ci, verbose = verbose, ...)
  attr(out, "object_name") <- .safe_deparse(substitute(x))
  out
}


#' @export
bci.get_predicted <- function(x, ...) {
  if ("iterations" %in% names(attributes(x))) {
    out <- hdi(as.data.frame(t(attributes(x)$iterations)), ...)
  } else {
    stop("No iterations present in the output.")
  }
  attr(out, "object_name") <- .safe_deparse(substitute(x))
  out
}

# Helper ------------------------------------------------------------------


#' @importFrom stats quantile
.bci <- function(x, ci, verbose = TRUE) {
  check_ci <- .check_ci_argument(x, ci, verbose)

  if (!is.null(check_ci)) {
    return(check_ci)
  }

  low <- (1 - ci) / 2
  high <- 1 - low
  sims <- length(x)
  z.inv <- length(x[x < mean(x, na.rm = TRUE)]) / sims

  z <- stats::qnorm(z.inv)
  U <- (sims - 1) * (mean(x, na.rm = TRUE) - x)
  top <- sum(U^3)
  under <- 6 * (sum(U^2))^1.5
  a <- top / under

  lower.inv <- stats::pnorm(z + (z + stats::qnorm(low)) / (1 - a * (z + stats::qnorm(low))))
  lower <- stats::quantile(x, lower.inv, names = FALSE)
  upper.inv <- stats::pnorm(z + (z + stats::qnorm(high)) / (1 - a * (z + stats::qnorm(high))))
  upper <- stats::quantile(x, upper.inv, names = FALSE)

  data.frame(
    "CI" = ci,
    "CI_low" = lower,
    "CI_high" = upper
  )
}