Conditional Beta distribution in R2WinBUGS How can I write in R2WinBUGS that V given U follows a beta distribution, i.e $V|U=u  \sim Beta (\alpha,\beta)$ distribution? Please see the attached example code. From my understanding this assumes $V\sim Beta (\alpha,\beta)$, but I would like to model the conditional  $V|U=u$.
Can anyone help me with an example code?
set.seed(1)
U <- runif(100,0,1)  
V <- runif(100,0,1)
dat <- data.frame(U,V)  # these are my hypothetical data

# model

"model {
      for(i in 1:N)
        {
        V[i] ~ dbeta (alpha[i], beta[i])
        alpha[i] <- mu[i] * phi
        beta[i]  <- (1-mu[i]) * phi
        logit(mu[i]) = b0 + b1* U[i]
       }
  
  #priors
  phi ~ dgamma(0.1,0.1)
  b0 ~ dnorm(0,10)
  b1 ~ dnorm(0,10)
}
```

 A: Your code does model the conditional relationship $V|U$. Look at the lines
        V[i] ~ dbeta (alpha[i], beta[i])
        alpha[i] <- mu[i] * phi
        beta[i]  <- (1-mu[i]) * phi
        logit(mu[i]) = b0 + b1* U[i]

V[i] follows a beta distribution parametrized by alpha[i] and beta[i], where both of the parameters are defined in terms of mu[i] that is a function of U[i]. Similar kind of dependency is observed in linear regression or generalized linear models (e.g. logistic regression), where we model $y|X$, where $E[y|X] = f(X)$ with $f(\cdot)$ being the regression function.
As a sidenote, using WinBUGS in not a great idea. This software is not actively maintained for many years, the "latest news" section on its website has the newest entry from nine years ago, while the latest update predates it. If you use it, you must assume that it stops working any time and this is likely not to get fixed, making your code useless. For similar, but actively developed alternative you could check Stan.
