# This is file “nonlinearmodel.bug”
model{
  for( i in 1 : N ) {
    y[i] ~ dnorm(mu[i], tau)
    mu[i] <- alpha - beta * pow(gamma,x[i])
  }
  alpha ~ dnorm(0.0, 1.0E-6)
  beta ~ dnorm(0.0, 1.0E-6)
  gamma ~ dunif(0.0, 1.0)
  tau ~ dgamma(0.01, 0.01)
}


# Copy and paste the following lines into R.  In R, remember to go 
# to “file>change dir…” to enter the subdirectory where the file 
# “nonlinearmodel.bug” is located.  I might also want to certify 
# yourself where WinBUGS is located in your computer.

library(R2WinBUGS)

x = c(1.0,1.5,1.5,1.5,2.5,4.0,5.0,5.0,7.0,8.0,8.5,
      9.0,9.5,9.5,10.0,12.0,12.0,13.0,13.0,14.5,
      15.5,15.5,16.5,17.0,22.5,29.0,31.5)
y = c(1.80,1.85,1.87,1.77,2.02,2.27,2.15,2.26,2.47,
      2.19,2.26,2.40,2.39,2.41,2.50,2.32,2.32,2.43,
      2.47,2.56,2.65,2.47,2.64,2.56,2.70,2.72,2.57)
N     <- length(x)
data  <- list("x","y","N")

inits <- function(){
  list(alpha=1,beta=1,tau=1,gamma=0.9)
}

nonlinear.sim = bugs(data,inits,
     model.file="nonlinearmodel.bug",
     parameters=c("alpha","beta","tau","gamma"),
     n.chains=1,n.iter=20000,n.burnin=5000,n.thin=1,
     bugs.directory="c:/Program Files/WinBUGS14/",
     codaPkg=FALSE)

nonlinear.sim

names(nonlinear.sim)

dim(nonlinear.sim$sims.array)

nonlinear.sim$sims.array[1:15,1,]

par(mfrow=c(2,2))
ts.plot(nonlinear.sim$sims.array[,1,1],xlab="iterations",ylab="",main="alpha")
ts.plot(nonlinear.sim$sims.array[,1,2],xlab="iterations",ylab="",main="beta")
ts.plot(nonlinear.sim$sims.array[,1,3],xlab="iterations",ylab="",main="tau")
ts.plot(nonlinear.sim$sims.array[,1,4],xlab="iterations",ylab="",main="gamma")