Big data, machine learning and AI inverts adverse selection problems. It allows insurers to infer statistical information and thereby reverses information advantage from the insuree to the insurer. In a setting with two-dimensional type space whose correlation can be inferred with big data we derive three results: First, a novel tradeoff between a belief gap and price discrimination emerges. The insurer tries to protect its statistical information by offering only a few screening contracts. Second, we show that forcing the insurance company to reveal its statistical information can be welfare improving. Third, we show in a setting with naive agents that do not perfectly infer statistical information from the price of offered contracts, price discrimination significantly boosts insurer's profits. We also discuss the significance our analysis through three stylized facts: the rise of data brokers, the importance of consumer activism and regulatory forbearance, and merits of a public data repository.