# Need suggestion/guide on how to estimate unknown bayesian priors

Suppose I can only observe people who visit Starbucks. My posterior probabilities will be like $\Pr(\text{male} \mid \text{visits Starbucks})$, $\Pr(\text{has hair} \mid \text{visits Starbucks})$, etc. – where all of these are independently distributed. I want to use a naive Bayes classifier to analyze if the probability of someone visiting Starbucks is being dominated by one of those posteriors. Now the problem is, my entire data set is just of people who visit Starbucks, I cannot know the number of people who do not visit. Given this, how can I estimate the priors $\Pr(\text{visits Starbucks})$ and $\Pr(\text{Does not visit Starbucks})$?

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• You cannot estimate priors, they are part of your model. – Xi'an Mar 24 '17 at 10:07

Generically speaking, you can't. Imagine a world where every single person visits Starbucks ($\Pr(\text{visits Starbucks}) = 1$), and another where a uniformly random 1% of people do ($\Pr(\text{visits Starbucks}) = 0.01$). Your dataset would look the same either way. You're going to need some kind of outside information.