  We consider a scenario in which a database stores sensitive data of users and
an analyst wants to estimate statistics of the data. The users may suffer a
cost when their data are used in which case they should be compensated. The
analyst wishes to get an accurate estimate, while the users want to maximize
their utility. We want to design a mechanism that can estimate statistics
accurately without compromising users' privacy.
  Since users' costs and sensitive data may be correlated, it is important to
protect the privacy of both data and cost. We model this correlation by
assuming that a user's unknown sensitive data determines a distribution from a
set of publicly known distributions and a user's cost is drawn from that
distribution. We propose a stronger model of privacy preserving mechanism where
users are compensated whenever they reveal information about their data to the
mechanism. In this model, we design a Bayesian incentive compatible and privacy
preserving mechanism that guarantees accuracy and protects the privacy of both
cost and data.
