The noninformative prior in beta-binomial model

Considering a beta-binomial model:

y_i \sim Binomial(n_i, \theta_i) \\ \theta_i \sim \beta(\alpha, \beta)

I am sure the mean of \theta_i is not equal to 0.5. So \alpha \neq \beta. Now, how to determine the value of hyperparameters \alpha and \beta as noninformative priors?

Any help is appreciated!

\theta \sim \beta(\alpha,\beta)
E[\theta]=\alpha/(\alpha+\beta)
Set \alpha=\mu*s, \beta=(1-\mu)*s with \mu mean and s scaling parameter.
Then E[\theta]=\mu s / ((1-\mu)s+\mu s)=\mu

In Stan

mu = inv_logit(something);
y ~ beta_binomial(n, mu * phi, (1-mu) * phi);

Yes. I know reparameterize two shape parameters, \alpha and \beta, as mean parameter \phi and total count parameter,\lambda, is a normal approach. The Stan user guide gives the following noninformative prior:

phi ~ beta(1, 1); 
lambda ~ pareto(0.1, 1.5);

I tried multiple noninformative priors and found Haldane’s prior Beta (0,0) can not run.
How to solve the issue? Any help is appreciated!

\text{beta}(0, 0) is undefined, see, e.g.,

I don’t know the construction in question, but it sounds like a limit. If you can work out the density for the you can code it in Stan.

thank you for your advice!