## plain RMAP model

model {
	for (i in 1:(H+1)) {
		y[i] ~ dbinom(psi[i], n[i])
	
		psi[i] <- ilogit(theta[i])
	}

	for (i in 1:H) {
		theta[i] ~ dnorm(mu, tau.sq.inv)
	}

	theta[H+1] = theta_hist + theta_null

	theta_hist_lat ~ dnorm(mu, tau.sq.inv)
	theta_hist = theta_hist_lat*z
	theta_null_lat ~ dlogis(0, 1)
	theta_null = theta_null_lat*(1-z)

	z ~ dbern(0.5)

	mu ~ dlogis(0, 1)                    # logistic(0,1) on logit = uniform on probs
	tau ~ dt(0, pow(2.5, -2), 1) T(0,)   # half cauchy prior
	tau.sq.inv <- pow(tau, -2)
}
