model {
for (i in 1:5) {
y.rep[i] <- y
n.rep[i] <- n
y.rep[i] ~ dbin(theta[i], n.rep[i])
}

theta[1] ~ dunif(0,1) # uniform on theta
phi[1] ~ dlogis(0,1)

phi[2] ~ dunif(-5,5) # uniform on logit(theta)
logit(theta[2]) <- phi[2]

theta[3] ~ dbeta(0.5,0.5) # Jeffreys on theta
phi[3] <- logit(theta[3])

phi[4] ~ dnorm(0,0.5) # var=2, flat at theta = 0.5
logit(theta[4]) <- phi[4]

phi[5] ~ dnorm(0,0.368) # var=2.71, approx. logistic
logit(theta[5]) <- phi[5]
}

Data (a):
list(y = 0, n = 10)

Data (b):
list(y = 10, n = 100)

Results (a):
node mean sd MC error 2.5% median 97.5% start sample
phi[1] 0.02938 1.813 0.01891 -3.606 0.03623 3.682 1 10000
phi[2] -3.599 0.9526 0.01128 -4.939 -3.722 -1.548 1 10000
phi[3] -4.262 2.228 0.02188 -9.703 -3.822 -1.278 1 10000
phi[4] -2.301 0.8569 0.00908 -4.13 -2.24 -0.7856 1 10000
phi[5] -2.568 0.9715 0.009158 -4.66 -2.486 -0.8743 1 10000
theta[1] 0.08445 0.07812 7.362E-4 0.002548 0.0614 0.2951 1 10000
theta[2] 0.04095 0.04671 5.565E-4 0.007109 0.02361 0.1753 1 10000
theta[3] 0.0454 0.06105 5.883E-4 6.108E-5 0.02141 0.2178 1 10000
theta[4] 0.1142 0.07878 7.712E-4 0.01583 0.09622 0.3131 1 10000
theta[5] 0.0965 0.07642 6.701E-4 0.009377 0.07683 0.2944 1 10000

Results (b):
node mean sd MC error 2.5% median 97.5% start sample
phi[1] 0.01556 1.819 0.0194 -3.665 0.03004 3.654 1 10000
phi[2] -2.239 0.341 0.003229 -2.959 -2.23 -1.607 1 10000
phi[3] -2.195 0.3335 0.003214 -2.886 -2.179 -1.587 1 10000
phi[4] -2.123 0.3129 0.003014 -2.766 -2.109 -1.543 1 10000
phi[5] -2.149 0.3244 0.003155 -2.819 -2.138 -1.552 1 10000
theta[1] 0.1079 0.03084 3.468E-4 0.05591 0.1052 0.1754 1 10000
theta[2] 0.1003 0.02996 3.002E-4 0.04931 0.09712 0.167 1 10000
theta[3] 0.1041 0.03022 3.007E-4 0.05283 0.1017 0.1698 1 10000
theta[4] 0.1105 0.03003 2.891E-4 0.05921 0.1082 0.1761 1 10000
theta[5] 0.1082 0.0305 3.031E-4 0.0563 0.1055 0.1748 1 10000