model
{
for (i in 1:N)
{
y[i] ~ dbin(theta[i], n[i])
theta[i] ~ dbeta(alpha, beta)
}
phi ~ dnorm(0, .00001)
psi ~ dnorm(0, .00001)
beta <- exp(psi)/(exp(phi) + 1)
alpha <- exp(phi + psi)/(1 + exp(phi))
}

Data
list(y = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 
1, 1, 1, 1, 1, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 5, 2, 5, 2, 7, 
7, 3, 3, 2, 9, 10, 4, 4, 4, 4, 4, 4, 4, 10, 4, 4, 4, 5, 11, 12, 
5, 5, 6, 5, 6, 6, 6, 6, 16, 15, 15, 9, 4), n = c(20, 20, 20, 20, 20, 
20, 20, 19, 19, 19, 19, 18, 18, 17, 20, 20, 20, 20, 19, 19, 18, 
18, 27, 25, 24, 23, 20, 20, 20, 20, 20, 20, 10, 49, 19, 46, 17, 
49, 47, 20, 20, 13, 48, 50, 20, 20, 20, 20, 20, 20, 20, 48, 19, 
19, 19, 22, 46, 49, 20, 20, 23, 19, 22, 20, 20, 20, 52, 46, 47, 
24, 14), N = 71)

inits
list(theta = 
c(0.066716750850901, 0.93453113711439, 0.922022016253322, 0.726600881200284, 
0.136582516366616, 0.612637049285695, 0.465397195192054, 0.254315665457398, 
0.869157318258658, 0.822756075998768, 0.638009986141697, 0.315387879265472, 
0.08104378846474, 0.880352098261938, 0.519659409299493, 0.0947331613861024, 
0.146266383118927, 0.370500170392916, 0.348384690005332, 0.240447702351958, 
0.361823419574648, 0.999656028812751, 0.104886536253616, 0.219606446800753, 
0.710239537758753, 0.898913979995996, 0.0558607294224203, 0.781089353375137, 
0.834200511919335, 0.8570413577836, 0.845310053089634, 0.0164933532942086, 
0.131868634838611, 0.948748094961047, 0.885160937672481, 0.208320477511734, 
0.625427239574492, 0.462737964931875, 0.577707870630547, 0.150097413687035, 
0.082707297289744, 0.305045755580068, 0.333657464710996, 0.263756845146418, 
0.92589452629909, 0.950162646127865, 0.801825537811965, 0.275392017327249, 
0.825187959708273, 0.111336550442502, 0.486654590815306, 0.660684109898284, 
0.98937397543341, 0.369746152078733, 0.310822365572676, 0.693164214026183, 
0.723299415083602, 0.325595344416797, 0.0844096895307302, 0.620371457422152, 
0.187088923528790, 0.688469547545537, 0.76858000527136, 0.993429913884029, 
0.227926373481750, 0.726581451483071, 0.591751087689772, 0.145836108596995, 
0.887671059696004, 0.93961080093868, 0.198534187860787),
psi = 1, phi = 2)