#' (M)HC (A)llele-Based (D)ifferencing between (Pop)ulations
#'
#' Tools for the analysis of population differences using the Major Histocompatibility Complex (MHC) genotypes of samples having a variable number of alleles (1-4) recorded for each individual.
#' @details For a full tutorial see package vignette: \code{vignette("MADPop-quicktut")}.
#' @docType package
#' @name MADPop
#' @useDynLib MADPop, .registration = TRUE
#' @import Rcpp
#' @import methods
#' @importFrom rstan extract sampling
#' @examples
#' # typical dataset
#' head(fish215[sample(nrow(fish215)),])
#' table(fish215$Lake) # number of samples per lake
#'
#' # contingency table on two lakes
#' iLakes <- c("Michipicoten", "Simcoe")
#' Xsuff <- UM.suff(X = fish215[fish215$Lake %in% iLakes,])
#' ctab <- Xsuff$tab
#' ctab
#'
#' # bootstrapped p-value calculation for chi^2 and LR tests
#' p.MLE <- colSums(ctab)/sum(ctab)
#' N1 <- sum(ctab[1,])
#' N2 <- sum(ctab[2,])
#' # bootstrapped test statistics (chi^2 and LRT)
#' T.boot <- UM.eqtest(N1 = N1, N2 = N2, p0 = p.MLE, nreps = 1e3)
#'
#' # observed test statistics
#' T.obs <- c(chi2 = chi2.stat(ctab), LRT = LRT.stat(ctab))
#' # p-values
#' rowMeans(t(T.boot) > T.obs)
#'
#' # posterior sampler for hierarchical model
#'
#' # output posterior probability for each genotype in lake Simcoe
#' rhoId <- "Simcoe"
#' nsamples <- 500
#' hUM.fit <- hUM.post(nsamples = nsamples, X = fish215,
#'                     rhoId = rhoId, chains = 1)
#'
#' # first 20 genotype posterior probabilities in lake Simcoe
#' rho.post <- hUM.fit$rho[,1,]
#' boxplot(rho.post[,1:20], las = 2,
#'         xlab = "Genotype", ylab = "Posterior Probability",
#'         pch = ".", col = "grey")
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