Big data and AI invert classical adverse selection: insurers can now infer statistical correlations that consumers cannot, reversing the traditional informational advantage. We study insurance contracting where a two-dimensional state determines risk, the agent privately knows one dimension, and the insurer privately knows how the two correlate. The insurer faces a fundamental trade-off between obfuscation and price discrimination—fine-tuned contracts enable better screening but may reveal her statistical advantage. The optimal policy exhibits a bang-bang structure: pooling on a statistical model that renders the agent’s information worthless, and full disclosure elsewhere. Profits increase substantially when agents fail to perform Bayesian inference.