model{ 
#total<-sum(freqobs[1:8])

#Likelihood
freqobs[1:8]~dmulti(p[1:8],total) 

for (i in 1:8){
p[i]<-prev*(positive[i])+(1-prev)*(negative[i])
 
positive[i]<-(s[1]*test1[i]+(1-s[1])*(1-test1[i]))      #sensitivity(test1)
	   * (s[2]*test2[i]+(1-s[2])*(1-test2[i]))      #sensitivity(test2)
	   * (s[3]*test3[i]+(1-s[3])*(1-test3[i]))      #sensitivity(test3)

negative[i]<- ((1-x[1])*test1[i]+x[1]*(1-test1[i]))     #specificity(test1)
	    * ((1-x[2])*test2[i]+x[2]*(1-test2[i]))     #specificity(test2)
	    * ((1-x[3])*test3[i]+x[3]*(1-test3[i]))     #specificity(test3)
}

#Prior
#Test 3 specificity fixed at 97.2% (California sea lion example)
#noninformative priors used for other parameters in this example
#For simulations using arc points A-H, this is the value you would
  #fix to the specificity of the arc point selected
prev~dbeta(1,1)
s[3]~dbeta(1,1) 
x[3]<- 0.972 


for (j in 1:2){
s[j]~dbeta(1,1) 
x[j]~dbeta(1,1) }
#s[6]<-s[1]+s[2]-s[1]*s[2]

#Prediction
freqpred[1:8]~dmulti(p[1:8],total)

#Bayesian_p
for (i in 1:8){ pvalue[i]<-step(freqpred[i]-freqobs[i]) }
}