model {
  # allele frequencies into genotype frequencies
  p[1] <- p.a*p.a + f*p.a*(1-p.a)
  p[2] <- 2*p.a*p.b*(1-f) 
  p[3] <- 2*p.a*p.c*(1-f)
  p[4] <- p.b*p.b + f*p.b*(1-p.b)
  p[5] <- 2*p.b*p.c*(1-f)
  p[6] <- p.c*p.c + f*p.c*(1-p.c)

  # the likelihood
  n[1:6] ~ dmulti(p[], N)

  # priors
  # allele frequencies
  for (i in 1:3) {
    phi[i] ~ dgamma(1, 1)
  }
  sum.phi <- sum(phi[])
  p.a <- phi[1]/sum.phi
  p.b <- phi[2]/sum.phi
  p.c <- phi[3]/sum.phi
  # f
  w ~ dunif(0, 1)
  a.f <- max(-p.a/(1-p.a), -(1-p.a)/p.a)
  b.f <- max(-p.b/(1-p.b), -(1-p.b)/p.b)
  c.f <- max(-p.c/(1-p.c), -(1-p.c)/p.c)
  min.f.1 <- max(a.f, b.f)
  f.min <- max(min.f.1, c.f)
  f <- w*(1 - f.min) + f.min

  # sample size
  N <- sum(n[])
}

# data
list(n=c(0,4,1,13,7,0))