How to combine step(x) and dbern(p) in JAGS/WinBUGS?

Question

The problem involves trying to characterize the probability:

P.f = Pd*Pr{t1 < t2}

using jags or WinBUGS. The issue is the last term where both t1 and t2 are random variables. A sample, stripped down, model using this is given below and hopefully provides insight into what I am trying to do. As expected, I get an error indicating that I am redefining the variable 'y'. Searching for a trick to get past this is proving difficult.

Any insight would be appreciated!

FWIW, I've also posted a similar question on the WinBUGS list, but cross-posted here with the hope of reaching a wider audience.

---

model {         
    for(j in 1:N) {
        t.1[j] ~ dweib(alpha.1,lambda.1) 
        t.2[j] ~ dweib(alpha.2, lambda.2);
        p.det[j] ~ dbeta(a,b);
        y[j] <- step(t.2[j]-t.1[j]);            
        y[j] ~ dbern(py);
    }   
    alpha.1 ~ dgamma(0.3,0.0001); 
    lambda.1 ~ dnorm(0., 10000.);
    alpha.2 ~ dgamma(0.3,0.0001); 
    lambda.2 ~ dnorm(0., 10000.);   
    py ~ dbeta(0.3,0.3);
    a ~ dgamma(1, 0.01) 
    b ~ dgamma(1, 0.01) 
    pd ~ dbeta(a,b) 
    p.f<- pd*py
}

Answer 1

In JAGS, you can't reuse, in your case, y[j] as you sometimes can in WinBUGS. Instead, you create "new" data out of the data that you pass to JAGS in a data block at the top of the code (i.e., before the model step):

data {
  for (j in 1:N) {
    y[j] <- step(t.2[j] - t.1[j]) 
  }
}

You can then use y[j] on the left hand side of distributions in the model step:

model {
  for (j in 1:N) {
    ...
    y[j] ~ dbern(py)
    ...
  }
}

This can't be done in WinBUGS, however, as there's no data block; instead, you should just pass a precalculated variable y to WinBUGS.