  We build a Bayesian contextual classification model using an optimistic score
ratio for robust binary classification when there is limited information on the
class-conditional, or contextual, distribution. The optimistic score searches
for the distribution that is most plausible to explain the observed outcomes in
the testing sample among all distributions belonging to the contextual
ambiguity set which is prescribed using a limited structural constraint on the
mean vector and the covariance matrix of the underlying contextual
distribution. We show that the Bayesian classifier using the optimistic score
ratio is conceptually attractive, delivers solid statistical guarantees and is
computationally tractable. We showcase the power of the proposed optimistic
score ratio classifier on both synthetic and empirical data.
