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#' \code{updog} Flexible Genotyping for Polyploids
#'
#' Implements empirical Bayes approaches to genotype
#' polyploids from next generation sequencing data while
#' accounting for allele bias, overdispersion, and sequencing
#' error. The main functions are \code{\link{flexdog}()}
#' and \code{\link{multidog}()}, which allow the specification
#' of many different genotype distributions. Also provided
#' are functions to simulate genotypes, \code{\link{rgeno}()},
#' and read-counts, \code{\link{rflexdog}()}, as well as
#' functions to calculate oracle genotyping error rates,
#' \code{\link{oracle_mis}()}, and correlation with the true
#' genotypes, \code{\link{oracle_cor}()}. These latter two
#' functions are useful for read depth calculations. Run
#' \code{browseVignettes(package = "updog")} in R for example usage. See
#' Gerard et al. (2018)
#' <\doi{10.1534/genetics.118.301468}>
#' and Gerard and Ferrao (2020)
#' <\doi{10.1093/bioinformatics/btz852}>
#' for details on the implemented methods.
#'
#' The package is named \code{updog} for "Using
#' Parental Data for Offspring Genotyping" because
#' we originally developed the
#' method for full-sib populations, but it works
#' now for more general populations.
#'
#' Our best competitor is probably the \code{fitPoly} package,
#' which you can check out at
#' \url{https://cran.r-project.org/package=fitPoly}. Though, we think
#' that \code{updog} returns better calibrated measures of uncertainty
#' when you have next-generation sequencing data.
#'
#' If you find a bug or want an enhancement, please submit an
#' issue at \url{https://github.com/dcgerard/updog/issues}.
#'
#' @references
#' \itemize{
#' \item{Gerard, D., Ferrão, L. F. V., Garcia, A. A. F., & Stephens, M. (2018). Genotyping Polyploids from Messy Sequencing Data. \emph{Genetics}, 210(3), 789-807. \doi{10.1534/genetics.118.301468}.}
#' \item{Gerard, David, and Luís Felipe Ventorim Ferrão. "Priors for genotyping polyploids." Bioinformatics 36, no. 6 (2020): 1795-1800. \doi{10.1093/bioinformatics/btz852}.}
#' }
#'
#' @section \code{updog} Functions:
#' \describe{
#' \item{\code{\link{flexdog}()}}{The main function that
#' fits an empirical Bayes approach to genotype polyploids
#' from next generation sequencing data.}
#' \item{\code{\link{multidog}()}}{A convenience function for running
#' \code{\link{flexdog}()} over many SNPs. This function provides
#' support for parallel computing.}
#' \item{\code{\link{format_multidog}()}}{Return arrayicized elements from the output of \code{\link{multidog}()}.}
#' \item{\code{\link{filter_snp}()}}{Filter SNPs based on the output of \code{\link{multidog}()}}
#' \item{\code{\link{rgeno}()}}{simulate the genotypes of a sample
#' from one of the models allowed in \code{\link{flexdog}()}.}
#' \item{\code{\link{rflexdog}()}}{Simulate read-counts from the
#' \code{\link{flexdog}()} model.}
#' \item{\code{\link{plot.flexdog}()}}{Plotting the output of
#' \code{\link{flexdog}()}.}
#' \item{\code{\link{plot.multidog}()}}{Plotting the output of
#' \code{\link{multidog}()}.}
#' \item{\code{\link{oracle_joint}()}}{The joint distribution of the true genotype
#' and an oracle estimator.}
#' \item{\code{\link{oracle_plot}()}}{Visualize the output of \code{\link{oracle_joint}()}.}
#' \item{\code{\link{oracle_mis}()}}{The oracle misclassification error rate (Bayes rate).}
#' \item{\code{\link{oracle_cor}()}}{Correlation between the true genotype and the oracle estimated genotype.}
#' }
#'
#' @section \code{updog} Datasets:
#' \describe{
#' \item{\code{\link{snpdat}}}{A small example dataset for using
#' \code{\link{flexdog}}.}
#' \item{\code{\link{uitdewilligen}}}{A small example dataset}
#' }
#'
#' @useDynLib updog
#' @importFrom Rcpp sourceCpp
#' @importFrom RcppArmadillo armadillo_version
#' @importFrom ggplot2 ggplot
#' @importFrom assertthat assert_that
#' @importFrom foreach %dopar%
#' @importFrom doRNG %dorng%
#' @import doFuture
#' @importFrom foreach foreach
#' @importFrom methods as
#'
#' @docType package
#' @name updog-package
#' @aliases updog
#'
#' @author David Gerard
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#' The Beta-Binomial Distribution
#'
#' Density, distribution function, quantile function and random generation
#' for the beta-binomial distribution when parameterized
#' by the mean \code{mu} and the overdispersion parameter \code{rho}
#' rather than the typical shape parameters.
#'
#'
#' Let \eqn{\mu} and \eqn{\rho} be the mean and overdispersion parameters.
#' Let \eqn{\alpha} and \eqn{\beta} be the usual shape parameters of
#' a beta distribution. Then we have the relation
#' \deqn{\mu = \alpha/(\alpha + \beta),}
#' and
#' \deqn{\rho = 1/(1 + \alpha + \beta).}
#' This necessarily means that
#' \deqn{\alpha = \mu (1 - \rho)/\rho,}
#' and
#' \deqn{\beta = (1 - \mu) (1 - \rho)/\rho.}
#'
#' @param x,q A vector of quantiles.
#' @param p A vector of probabilities.
#' @param n The number of observations.
#' @param size A vector of sizes.
#' @param mu Either a scalar of the mean for each observation,
#' or a vector of means of each observation, and thus
#' the same length as \code{x} and \code{size}. This must
#' be between 0 and 1.
#' @param rho Either a scalar of the overdispersion parameter
#' for each observation, or a vector of overdispersion
#' parameters of each observation, and thus the same length as
#' \code{x} and \code{size}. This must be between 0 and 1.
#' @param log,log_p A logical vector either of length 1 or the same
#' length as \code{x} and \code{size}. This determines whether
#' to return the log probabilities for all observations
#' (in the case that its length is 1) or for
#' each observation (in the case that
#' its length is that of \code{x} and \code{size}).
#'
#' @name betabinom
#'
#' @author David Gerard
#'
#' @return Either a random sample (\code{rbetabinom}),
#' the density (\code{dbetabinom}), the tail
#' probability (\code{pbetabinom}), or the quantile
#' (\code{qbetabinom}) of the beta-binomial distribution.
#'
#' @examples
#' x <- rbetabinom(n = 10, size = 10, mu = 0.1, rho = 0.01)
#' dbetabinom(x = 1, size = 10, mu = 0.1, rho = 0.01, log = FALSE)
#' pbetabinom(q = 1, size = 10, mu = 0.1, rho = 0.01, log_p = FALSE)
#' qbetabinom(p = 0.6, size = 10, mu = 0.1, rho = 0.01)
#'
#'
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