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

[example-5_2_1-surgery-sensitivity0]
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

[example-5_2_1-surgery-sensitivity1]