Two points:

1. Bayesian statistics allows use of "uninformative" priors. 2. Discarding your subjective beliefs is less than ideal as well as overweighting them. You have beliefs due to your experience. Weight them lightly but still use them. In the absence of much information your calculations will follow your gut. What else do you have in the absence of other information?

Using quantified subjective beliefs at least has the advantage of enabling you to make consistent choices based on what you know within a rigorously defined framework.