I am relatively new to statistical modeling, and I apologize if this question is somewhat basic. I am currently working with Bayesian models, specifically a stochastic model based on an Ornstein-Uhlenbeck process, and I am trying to determine the best uninformative prior for parameters on the log-odds scale.
Initially, I started with a $\mathcal{N}(0,1)$ prior for the parameters on the log-odds scale. However, I found that this prior is too informative for my needs. I then considered increasing the standard deviation of the prior, but I noticed that this made the prior even more informative. When the parameter is transformed back to the probability scale, a higher standard deviation seems to push the prior values more towards 0 and 1, which intuitively means a more informative prior. On the other hand, reducing the standard deviation concentrates the values more around the mean on the log-odds scale, which also seems to make the prior more informative in a different way.
Given this, I am unsure which prior to use for my parameters to ensure that it is as uninformative as possible. Could someone explain the best practices for choosing uninformative priors on the log-odds scale?
