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Consider the problem of estimating the probability of a person being interested in becoming a customer of a service or a buyer of a product, and only data about the current customers is available, that is, there is no information about the rejection of such product or service. Also, we are considering only one product, so collaborative filtering is unfeasible.

The initial idea is to use the Bayes theorem

$p(sell|\Theta) = \frac{p(\Theta|sell) p(sell)}{p(\Theta)}$

where $p(\Theta|sell) p(sell)$ is the distribution of the current customer data, and $p(\Theta)$ is general demographic information (income distribution in the region of interest, population pyramid, etc).

Is there any published work regarding this problem?

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