We consider the problem of detecting and quantifying the periodic component
of a function given noise-corrupted observations of a limited number of
input/output tuples. Our approach is based on Gaussian process regression which
provides a flexible non-parametric framework for modelling periodic data. We
introduce a novel decomposition of the covariance function as the sum of
periodic and aperiodic kernels. This decomposition allows for the creation of
sub-models which capture the periodic nature of the signal and its complement.
To quantify the periodicity of the signal, we derive a periodicity ratio which
reflects the uncertainty in the fitted sub-models. Although the method can be
applied to many kernels, we give a special emphasis to the Mat\'ern family,
from the expression of the reproducing kernel Hilbert space inner product to
the implementation of the associated periodic kernels in a Gaussian process
toolkit. The proposed method is illustrated by considering the detection of
periodically expressed genes in the arabidopsis genome.Comment: in PeerJ Computer Science, 201
