  We propose a Bayesian approach to detect multiple change-points in a
piecewise-constant signal corrupted by a functional part corresponding to
environmental or experimental disturbances. The piecewise constant part (also
called segmentation part) is expressed as the product of a lower triangular
matrix by a sparse vector. The functional part is a linear combination of
functions from a large dictionary. A Stochastic Search Variable Selection
approach is used to obtain sparse estimations of the segmentation parameters
(the change-points and the means over the segments) and of the functional part.
The performance of our proposed method is assessed using simulation
experiments. Applications to two real datasets from geodesy and economy fields
are also presented.
