Negative binomial , Poisson-gamma mixture winbugs

Question

Winbugs trap error

1. • model
     {
     for (i in 1:5323) {
     Y[i] ~ dpois(mu[i])  # NB model as a Poisson-gamma mixture
     mu[i] ~ dgamma(b[i], a[i])  # NB model as a poisson-gamma mixture
     a[i] <- b[i] / Emu[i]
     b[i] <- B * X[i]
     Emu[i] <- beta0 * pow(X[i], beta1)  # model equation
     }
     
     # Priors
     beta0 ~ dunif(0,10)  # parameter
     beta1 ~ dunif(0,10)   # parameter
     B ~ dunif(0,10)  # over-dispersion parameter
     }
     
     X[]    Y[]
     1.5    0
     2.9    0
     1.49   0
     0.39   0
     3.89   0
     2.03   0
     0.91   0
     0.89   0
     0.97   0
     2.16   0
     0.04   0
     1.12   1s
     2.26   0
     3.6    1
     1.94   0
     0.41   1
     2  0
     0.9    0
     0.9    0
     0.9    0
     0.1    0
     0.88   1
     0.91   0
     6.84   2
     3.14   3
     End ```
     
     
     

• This is just a sample of the data, the model question is coming from Ezra Hauer 8.3.2, the art of regression of road safety, the model is providing an **error undefined real result. **

• The aim of model is to fully Bayesian and a one step model and not use empirical bayes.

• The results should be similar to MLE where beta0 is 1.65, beta1 0.871, overdispersion is 0.531

• X is the only variable and y is actual collision, So X cannot be zero or negative, while y cannot be lower than zero, if the model in solved as Poisson gamma mixture using maximum likelihood then it can be created

• How can I make this model work

• Solving an error in winbugs?

Answer 1

the data is in excel, the model worked fine when I selected the biggest 1000 observations only.