A Bayesian Method for Causal Modeling and Discovery Under Selection
  This paper describes a Bayesian method for learning causal networks using
samples that were selected in a non-random manner from a population of
interest. Examples of data obtained by non-random sampling include convenience
samples and case-control data in which a fixed number of samples with and
without some condition is collected; such data are not uncommon. The paper
describes a method for combining data under selection with prior beliefs in
order to derive a posterior probability for a model of the causal processes
that are generating the data in the population of interest. The priors include
beliefs about the nature of the non-random sampling procedure. Although exact
application of the method would be computationally intractable for most
realistic datasets, efficient special-case and approximation methods are
discussed. Finally, the paper describes how to combine learning under selection
with previous methods for learning from observational and experimental data
that are obtained on random samples of the population of interest. The net
result is a Bayesian methodology that supports causal modeling and discovery
from a rich mixture of different types of data.
