  We propose a multiresolution Gaussian process to capture long-range,
non-Markovian dependencies while allowing for abrupt changes. The
multiresolution GP hierarchically couples a collection of smooth GPs, each
defined over an element of a random nested partition. Long-range dependencies
are captured by the top-level GP while the partition points define the abrupt
changes. Due to the inherent conjugacy of the GPs, one can analytically
marginalize the GPs and compute the conditional likelihood of the observations
given the partition tree. This property allows for efficient inference of the
partition itself, for which we employ graph-theoretic techniques. We apply the
multiresolution GP to the analysis of Magnetoencephalography (MEG) recordings
of brain activity.
