  Many time series problems feature epidemic changes - segments where a
parameter deviates from a background baseline. The number and location of such
changes can be estimated in a principled way by existing detection methods,
providing that the background level is stable and known. However, practical
data often contains nuisance changes in background level, which interfere with
standard estimation techniques. Furthermore, such changes often differ from the
target segments only in duration, and appear as false alarms in the detection
results. To solve these issues, we propose a two-level detector that models and
separates nuisance and signal changes. As part of this method, we developed a
new, efficient approach to simultaneously estimate unknown, but fixed,
background level and detect epidemic changes. The analytic and computational
properties of the proposed methods are established, including consistency and
convergence. We demonstrate via simulations that our two-level detector
provides accurate estimation of changepoints under a nuisance process, while
other state-of-the-art detectors fail. Using real-world genomic and demographic
datasets, we demonstrate that our method can identify and localise target
events while separating out seasonal variations and experimental artefacts.
