A nonparametric approach for relevance determination
Babak Shahbaba · arXiv (Cornell University) · 2010
The objective of many high throughput studies is to identify factors that are relevant to an outcome of interest. Such studies are abundant in genetics, image processing, astrophysics, and neuroscience. In this paper, we argue that treating these problems as large-scale hypothesis tests does not reflect the motivation behind the studies. Instead, we suggest treating these studies as a decision problem, where our primary concern is selecting the most relevant set of factors for a more focused follow up. Furthermore, instead of dividing the factors into a significant and a non-significant group (which is common in the hypothesis testing framework), we propose a flexible Bayesian model that accommodates subgroups with different degrees of importance. To this end, our approach uses a simple extension of Dirichlet process mixtures to model the relationship between the factors and the outcome. With simulated data, we demonstrate that our model performs substantially better than alternative methods based on the false discovery rate. We also apply our method to two real large-scale studies. The objective of the first study is to interrogate the mutation status of p53 in cancer cell lines, and the objective of the second study is to identify differentially expressed genes between two types of leukemia. Overall, we find that taking into account the true motivation behind high throughput studies and the possible complexity of relationships between factors and outcome could improve the analysis by increasing the rate of discovering relevant factors while keeping the false discovery rate low.