A Bayesian Method for Causal Modeling and Discovery Under Selection

Abstract

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.