This time I target the following two-class Bayesian logistic regression as statistical models.
$$y_n \sim \mathrm{Bernoulli}(q_n)$$ $$q_n = \sigma (\beta_0 + x_n \beta_1)$$
where $n$ is the index of the data and $\sigma$ is the logistic function.
Since I assume $\beta_0 + x_n \beta_1$ as the linear predictor (the independent variable of the logistic activation function), I have two parameters $\beta_0$ and $\beta_1$, and I want to express that their prior distributions independently follow an improper uniform distribution, the support of which each probability density function is the set of real numbers. Is it appropriate to write
$$\beta_0, \beta_1 \sim \mathrm{Uniform}(-\infty, \infty), i.i.d.$$
in this case? I'm particularly concerned about the appropriateness of writing i.i.d. If there is a more appropriate way to express this, please let me know.