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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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    $\begingroup$ Welcome to Cross Validated! Please take a moment to view our tour. $\endgroup$ – Tavrock Mar 22 '17 at 19:30
  • $\begingroup$ You cannot estimate priors, they are part of your model. $\endgroup$ – Xi'an Mar 24 '17 at 10:07
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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.

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  • $\begingroup$ Yes, my problem is i cannot count the number of people who dont visit - as that number is too large to get reliable estimates. I am not saying i cant get outside information, I want to know how/ or what kind of information i need to solve this. $\endgroup$ – Harry Lincoln Komol Mar 22 '17 at 19:29
  • $\begingroup$ I think we'll have to know a little more about the specific situation to be useful.... $\endgroup$ – Danica Mar 22 '17 at 19:31

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