Also, in case anyone is interested, the uninformative Jeffreys prior for this in Bayesian statistics (meaning it does not assume anything and is invariant to ce

Also, in case anyone is interested, the uninformative Jeffreys prior for this in Bayesian statistics (meaning it does not assume anything and is invariant to certain transformations of the inputs) is Beta(0.5, 0.5). Thus the initial guess is 0.5, and it evolves from there from the data.