model {
	mu ~ dunif(0,1)
 	t~dt(0,1,2)
        tau<-abs(t)
        alpha<-mu*tau
        beta<-(1-mu)*tau

	psi ~ dunif(0,1)
	for(i in 1:M){
		z[i]~dbin(psi,1)
		p[i]~dbeta(alpha,beta)
		zp[i]<-p[i]*z[i]
		x[i] ~ dbin(zp[i],T)
	}
	N<-sum(z[]) 
}