model {

psi~dunif(0,1)  # sample inclusion probability/ for data aug
sigma1~dunif(0,10)
sigma2~dunif(0,10)
tau1<-1/(sigma1*sigma1)
tau2<-1/(sigma2*sigma2)
p~dunif(0,1)

for(i in 1:(nind+nzeroes)){
 z[i]~dbin(psi,1)   # inclusion indicator
 s1[i]~dunif(Xl,Xu)
 s2[i]~dunif(Yl,Yu)

  for(t in 1:T){
   # compute whether individual is in plot at t
   # delta defines the polygon within which centers are
   # distributed
    flag1[i,t]<-step(U1[i,t]-(Xl+delta))
    flag2[i,t]<- step( (Xu-delta) - U1[i,t])
    flag3[i,t]<- step(U2[i,t] - (Yl+delta))
    flag4[i,t]<- step( (Yu-delta)-U2[i,t])
    inplot[i,t]<-flag1[i,t]*flag2[i,t]*flag3[i,t]*flag4[i,t]

   # if a member of population and inplot, then subject to sampling
    mu[i,t]<-inplot[i,t]*z[i]*p
    U1[i,t]~dnorm(s1[i],tau1)I(Xl,Xu)
    U2[i,t]~dnorm(s2[i],tau2)I(Yl,Yu)
    Y[i,t]~dbern(mu[i,t])
  }
}

}