  Genomic phenotypes, such as DNA methylation and chromatin accessibility, can
be used to characterize the transcriptional and regulatory activity of DNA
within a cell. Recent technological advances have made it possible to measure
such phenotypes very densely. This density often results in spatial structure,
in the sense that measurements at nearby sites are very similar.
  In this paper, we consider the task of comparing genomic phenotypes across
experimental conditions, cell types, or disease subgroups. We propose a new
method, Joint Adaptive Differential Estimation (JADE), which leverages the
spatial structure inherent to genomic phenotypes. JADE simultaneously estimates
smooth underlying group average genomic phenotype profiles, and detects regions
in which the average profile differs between groups. We evaluate JADE's
performance in several biologically plausible simulation settings. We also
consider an application to the detection of regions with differential
methylation between mature skeletal muscle cells, myotubes and myoblasts.
