Abstract A seller with unlimited inventory of a digital good interacts with potential buyers with i.i.d. valuations. The seller can adaptively quote prices to each buyer to maximize long-term profits, but does not know the valuation distribution exactly. Under a linear demand model, we consider two information settings: partially censored, where agents who buy reveal their true valuations after the purchase is completed, and completely censored, where agents never reveal their valuations. In the partially censored case, we prove that myopic pricing with a Pareto prior is Bayes optimal and has finite regret. In both settings, we evaluate the myopic strategy against more sophisticated look-aheads using three valuation distributions generated from real data on auctions of physical goods, keyword auctions, and user ratings, where the linear demand assumption is clearly violated. For some datasets, complete censoring actually helps, because the restricted data acts as a “regularizer” on the posterior, preventing it from being affected too much by outliers.