model {
   P[1:2] ~ ddirch(A[1:2])
   for( i in 1 : N ) {
      w[i] ~ dcat(P[1:2])
      p[i] ~ dbeta(alpha[w[i]],beta[w[i]])
      r[i] ~ dbin(p[i],n[i])
      #proba. d'appartenance ? la pop. 2
	  proba2[i]<-step(w[i]-2) 		
      }
   for( j in 1 : 2 ) {   
        ppred[j] ~ dbeta(alpha[j],beta[j])
	    # relation entre (alpha, beta) et (p.mean,taille)		
   	 alpha[j]<-p.mean[j]*taille[j]
        beta[j]<-(1-p.mean[j])*taille[j]
	    # lois a priori sur taille[1] et taille[2]	
        taille[j]~dexp(0.001) 
# relation entre (alpha, beta) et (p.mean, rho)
# alpha[j]<-(1-rho[j])*p.mean[j]/rho[j]
# beta[j]<-(1-rho[j])*(1-p.mean[j])/rho[j]
        }
       # prior sur la pr?valence moy. g?n?rale pop. 1
       p.mean[1]~dbeta(2,18) 
 #prior sur la correlation intra-classe dans la pop. 1
 #rho[1]~dbeta(1,9)	
       # prior sur la pr?valence moy. g?n?rale pop. 2
       p.mean[2]~dbeta(1,1)
 #prior sur la correlation intra-classe dans la pop. 1
 #rho[2]~dbeta(1,1)	
}

list(N=91,A=c(1,1),n=c(600,415,276,220,150,142,120,100,100,85,84,71,69,55,50,50,40,32,20,1227053,635,4046,340,169,964,317,
445,134,256,252,939,187,59,426,100,100,100,98,190,560,540,1720,290,236,300,2511,123,177,361,350,561,80,150,100,50,50,292,337,48,137,589,220,100,2009,256,961,113,315,69,100,1409,80,200,81,
50,445,30,100,124,121,640,176,97,77,16,51,17,14,16,95,21),
r=c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,278,2,14,2,1,9,4,6,2,4,4,15,3,1,8,2,2,2,2,4,14,14,47,8,7,9,79,4,6,13,13,21,3,6,4,2,2,12,14,2,6,29,11,5,102,13,50,6,17,4,6,85,5,14,6,4,38,3,12,15,15,90,27,15,14,3,10,5,6,7,43,17),w=c(NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,1,
NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA
,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,2))

#pour la seconde param?trisation
#list(p.mean=c(0.05,0.5),rho=c(0,1,0.5)