I'm using Bayes theorem to classify data into two groups, where the conditional probability is known but the prior is not. So I assume that the ratio of prior probabilities is 1 and calculate the posterior probabilities. I then use the posterior probabilities to calculate a new prior, and I continue iterating until the difference in the ratio of instances of both groups between iterations is less than 1%.
I know this sounds kind of like "Bayesian updating", except I am not using new data, but iterating on the same set. For my problem this method works well, and it converges to a stable prior, but I don't know if this method has a name? Is it some special case of Bayesian inference? I also don't know if there is a good way of estimating error with this method.