#' Interpret Bayesian diagnostic indices
#'
#' Interpretation of Bayesian diagnostic indices, such as Effective Sample Size (ESS) and Rhat.
#'
#' @param ess Value or vector of Effective Sample Size (ESS) values.
#' @param rhat Value or vector of Rhat values.
#' @param rules A character string (see *Rules*) or a custom set of [rules()].
#'
#' @section Rules:
#'
#' ## ESS
#' - Bürkner, P. C. (2017) (`"burkner2017"`; default)
#'   - **ESS < 1000** - Insufficient
#'   - **ESS >= 1000** - Sufficient
#'
#' ## Rhat
#' - Vehtari et al. (2019) (`"vehtari2019"`; default)
#'   - **Rhat < 1.01** - Converged
#'   - **Rhat >= 1.01** - Failed
#' - Gelman & Rubin (1992) (`"gelman1992"`)
#'   - **Rhat < 1.1** - Converged
#'   - **Rhat >= 1.1** - Failed
#'
#'
#' @examples
#' interpret_ess(1001)
#' interpret_ess(c(852, 1200))
#'
#' interpret_rhat(1.00)
#' interpret_rhat(c(1.5, 0.9))
#' @references
#' \itemize{
#'   \item Bürkner, P. C. (2017). brms: An R package for Bayesian multilevel models using Stan. Journal of Statistical Software, 80(1), 1-28.
#'   \item Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
#'   \item Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2019). Rank-normalization, folding, and localization: An improved Rhat for assessing convergence of MCMC. arXiv preprint arXiv:1903.08008.
#' }
#' @export
interpret_ess <- function(ess, rules = "burkner2017") {
  rules <- .match.rules(
    rules,
    list(
      burkner2017 = rules(c(1000), c("insufficient", "sufficient"), name = "burkner2017", right = FALSE)
    )
  )

  interpret(abs(ess), rules)
}



#' @rdname interpret_ess
#' @export
interpret_rhat <- function(rhat, rules = "vehtari2019") {
  rules <- .match.rules(
    rules,
    list(
      vehtari2019 = rules(c(1.01), c("converged", "failed"), name = "vehtari2019"),
      gelman1992 = rules(c(1.1), c("converged", "failed"), name = "gelman1992")
    )
  )

  interpret(abs(rhat), rules)
}
