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#' Hardy-Weinberg equlibrium test for a multiallelic marker using JAGS
#'
#' @param k number of alleles.
#' @param n a vector of k(k+1)/2 genotype counts.
#' @param delta initial parameter values.
#' @param lambda initial parameter values.
#' @param lambdamu initial parameter values.
#' @param lambdasd initial parameter values.
#' @param parms monitored parmeters.
#' @param ... parameters passed to jags, e.g., n.chains, n.burnin, n.iter.
#'
#' @details
#' Hardy-Weinberg equilibrium test.
#'
#' This function performs Bayesian Hardy-Weinberg equilibrium test, which mirrors [hwe.hardy],
#' another implementation for highly polymorphic markers when asymptotic results do not hold.
#'
#' @export
#' @return The returned value is a fitted model from jags().
#'
#' @references
#' \insertRef{wakefield10}{gap}
#'
#' @seealso [`hwe.hardy`]
#'
#' @examples
#' \dontrun{
#' ex1 <- hwe.jags(4,c(5,6,1,7,11,2,8,19,26,15))
#' print(ex1)
#' ex2 <- hwe.jags(2,c(49,45,6))
#' print(ex2)
#' ex3 <- hwe.jags(4,c(0,3,1,5,18,1,3,7,5,2),lambda=0.5,lambdamu=-2.95,lambdasd=1.07)
#' print(ex3)
#' ex4 <- hwe.jags(9,c(1236,120,3,18,0,0,982,55,7,249,32,1,0,12,0,2582,132,20,1162,29,
#' 1312,6,0,0,4,0,4,0,2,0,0,0,0,0,0,0,115,5,2,53,1,149,0,0,4),
#' delta=c(1,1,1,1,1,1,1,1,1),lambdamu=-4.65,lambdasd=0.21)
#' print(ex4)
#' ex5 <- hwe.jags(8,n=c(
#' 3,
#' 4, 2,
#' 2, 2, 2,
#' 3, 3, 2, 1,
#' 0, 1, 0, 0, 0,
#' 0, 0, 0, 0, 0, 1,
#' 0, 0, 1, 0, 0, 0, 0,
#' 0, 0, 0, 2, 1, 0, 0, 0))
#' print(ex5)
#'
#' # Data and code accordining to the following URL,
#' # http://darwin.eeb.uconn.edu/eeb348-notes/testing-hardy-weinberg.pdf
#' hwe.jags.ABO <- function(n,...)
#' {
#' hwe <- function() {
#' # likelihood
#' pi[1] <- p.a*p.a + 2*p.a*p.o
#' pi[2] <- 2*p.a*p.b
#' pi[3] <- p.b*p.b + 2*p.b*p.o
#' pi[4] <- p.o*p.o
#' n[1:4] ~ dmulti(pi[],N)
#' # priors
#' a1 ~ dexp(1)
#' b1 ~ dexp(1)
#' o1 ~ dexp(1)
#' p.a <- a1/(a1 + b1 + o1)
#' p.b <- b1/(a1 + b1 + o1)
#' p.o <- o1/(a1 + b1 + o1)
#' }
#' hwd <- function() {
#' # likelihood
#' pi[1] <- p.a*p.a + f*p.a*(1-p.a) + 2*p.a*p.o*(1-f)
#' pi[2] <- 2*p.a*p.b*(1-f)
#' pi[3] <- p.b*p.b + f*p.b*(1-p.b) + 2*p.b*p.o*(1-f)
#' pi[4] <- p.o*p.o + f*p.o*(1-p.o)
#' n[1:4] ~ dmulti(pi[],N)
#' # priors
#' a1 ~ dexp(1)
#' b1 ~ dexp(1)
#' o1 ~ dexp(1)
#' p.a <- a1/(a1 + b1 + o1)
#' p.b <- b1/(a1 + b1 + o1)
#' p.o <- o1/(a1 + b1 + o1)
#' f ~ dunif(0,1)
#' }
#' N <- sum(n)
#' ABO.hwe <- R2jags::jags(list(n=n,N=N),,c("pi","p.a","p.b","p.o"),hwe,...)
#' ABO.hwd <- R2jags::jags(list(n=n,N=N),,c("pi","p.a","p.b","p.o","f"),hwd,...)
#' invisible(list(hwe=ABO.hwe,hwd=ABO.hwd))
#' }
#' hwe.jags.ABO.results <- hwe.jags.ABO(n=c(862, 131, 365, 702))
#' hwe.jags.ABO.results
#' }
#'
#' @author Jing Hua Zhao, Jon Wakefield
#' @keywords htest
hwe.jags <- function(k,n,delta=rep(1/k,k),lambda=0,lambdamu=-1,lambdasd=1,
parms=c("p","f","q","theta","lambda"), ...)
{
ncell <- k*(k+1)/2
N <- sum(n)
data <- list(k=k,n=n,ncell=ncell,N=N,lambdamu=lambdamu,lambdasd=lambdasd)
inits <- function() list(delta=delta,lambda=lambda)
modelfile <- system.file(package="gap","JAGS","hwe.jags")
jagsfit <- R2jags::jags(data, inits, parms, modelfile, ...)
}
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