  High stakes classification refers to classification problems where
erroneously predicting the wrong class is very bad, but assigning "unknown" is
acceptable. We make the argument that these problems require us to give
multiple unknown classes, to get the most information out of our analysis. With
imperfect data we refer to covariates with a large number of missing values,
large noise variance, and some errors in the data. The combination of high
stakes classification and imperfect data is very common in practice, but it is
very difficult to work on using current methods.
  We present a one-class classifier (OCC) to solve this problem, and we call it
NBP. The classifier is based on Naive Bayes, simple to implement, and
interpretable. We show that NBP gives both good predictive performance, and
works for high stakes classification based on imperfect data.
  The model we present is quite simple; it is just an OCC based on density
estimation. However, we have always felt a big gap between the applied
classification problems we have worked on and the theory and models we use for
classification, and this model closes that gap. Our main contribution is the
motivation for why this model is a good approach, and we hope that this paper
will inspire further development down this path.
