WinBUGS: Nonlinear regression model

Revisiting Example 3.7 (pages 102-3) on non-linear regression with exponential decay

y_i ~ N(b₁- b₁exp(-b₂x_i),t ^-2)

where y are oxygen concentrations and x are the number of days the experiments are carried out.

Data: x = (1,2,3,4,5,7) and y = (8.3,10.3,19,16,15.6,19.8).

Prior: p( b₁,b₂,t²) = p( b₁) p( b₂) p(t²) and

β₁ ~ U(-20,50)

β₂ ~ U(-2,6)

t² ~ G(0.001,0.001)

WINBUGS CODE FOR THE NONLINEAR MODEL

# NONLINEAR MODEL

model{

for (i in 1:N){

mu[i] <- beta1*(1-exp(-beta2*x[i]))

y[i]~dnorm(mu[i],tau2)

}

beta1~dunif(-20,50)

beta2~dunif(-2,6)

tau2 ~ dgamma(0.001,0.001)

}

# DATA

list(x=c(1,2,3,4,5,7),y=c(8.3,10.3,19,16,15.6,19.8),N=6)

# 2 SETS OF INITIAL VALUES

list(beta1=18,beta2=1.78,tau2=1)

list(beta1=-10,beta2=0,tau2=1)