[dugongs0]     Dugongs: nonlinear growth curve

Carlin and Gelfand (1991) present a nonconjugate Bayesian analysis of the following data set from Ratkowsky (1983):
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The data are length and age measurements for 27 captured dugongs (sea cows). Carlin and Gelfand (1991) model this data using a nonlinear growth curve with no inflection point and an asymptote as X i tends to infinity:

   Y i ~ Normal( m i , t ),   i = 1,...,27
   
    m i = a - bg Xi     a , b > 0; 0 < g < 1

Standard noninformative priors are adopted for a , b and t , and a uniform prior on (0,1) is assumed for g . However, this specification leads to a non conjugate full conditional distribution for g which is also non log-concave. The graph and corresponding BUGS code is given below


[dugongs2]


   model
   {
      for( i in 1 : N ) {
         Y[i] ~ dnorm(mu[i], tau)
         mu[i] <- alpha - beta * pow(gamma,x[i])   
      }
      alpha ~ dflat()T(0,)
      beta ~ dflat()T(0,)
      gamma ~ dunif(0.5, 1.0)
      tau ~ dgamma(0.001, 0.001)
      sigma <- 1 / sqrt(tau)
      U3 <- logit(gamma)   
   }

 Data ( click to open )


Inits for chain 1       Inits for chain 2    ( click to open )

Results

A 1000 update burn in followed by a further 10000 updates gave the parameter estimates

[dugongs3]