Bayesian model predictions I am using an exponential decay model for the prediction of chemical exposures. y[i] is measured exposure, and y_new[i] is a prediction for x_new. I expect that new predictions will have exponential decay.
model
{
for( i in 1 : Ndata ) {
    y[i] ~ dnorm( beta0*exp(beta1*x[i]) , tau )
    y_new[i] ~ dnorm( beta0*exp(beta1*x_new[i]) , tau )
}
beta0 ~ dunif( 0 , 200000)
beta1 ~ dunif(-1.0E+4,0)
tau <-1/(sigma*sigma)
sigma ~ dunif( 1.0E-4 , 1.0E+4 )
}

However, some predictions are negative numbers. How is that possible? Shouldn't all predictions for exponential decay be positive? How to explain negative values, if in reality, they are not possible.
I appreciate any help.

Your predictions are modeled to have normal error ie $y_{new} \sim N(\mu, \tau)$ where $\mu=\beta_0 * \exp{(\beta_1 * x_{new})}$ so for $\mu$ small this can easily result in negative values for $y_{new}$.
