Non Parametric Methods for Genomic Inference

This paper grew out of a number of examples arising in data coming from the ENCODE project (Birney et al., 2007). Variations of some of the methods described here have been applied at various places in that paper, as well as in Margulies et al., 2007, for assessing significance and computing confidence bounds for statistics that operate along a genomic sequence. The background on these methods are described in cookbook form in the supplements to these papers, and it is the goal of this paper to describe them in more detail and rigor. We begin with some concrete examples from the data mentioned in the papers above as well as other types of genomic data in Section 1.2, and proceed with a motivated description of our model in Section 2. Our methods are discussed both qualitatively and mathematically in Sections 3 and 4. Sections 5 contain results from simulation studies and real data analysis. Finally, an appendix with proofs of theorems stated in Sections 3 and 4 completes the paper. Essentially, we will argue that, in making inference about statistics computed from “large” stretches of the genome, in the absence of real knowledge about the evolutionary path which led to the genome in question, the best