  In many areas of science one aims to estimate latent sub-population mean
curves based only on observations of aggregated population curves. By
aggregated curves we mean linear combination of functional data that cannot be
observed individually. We assume that several aggregated curves with linear
independent coefficients are available. More specifically, we assume each
aggregated curve is an independent partial realization of a Gaussian process
with mean modeled through a weighted linear combination of the disaggregated
curves. We model the mean of the Gaussian processes as a smooth function
approximated by a function belonging to a finite dimensional space ${\cal H}_K$
which is spanned by $K$ B-splines basis functions. We explore two different
specifications of the covariance function of the Gaussian process: one that
assumes a constant variance across the domain of the process, and a more
general variance structure which is itself modelled as a smooth function,
providing a nonstationary covariance function. Inference procedure is performed
following the Bayesian paradigm allowing experts' opinion to be considered when
estimating the disaggregated curves. Moreover, it naturally provides the
uncertainty associated with the parameters estimates and fitted values. Our
model is suitable for a wide range of applications. We concentrate on two
different real examples: calibration problem for NIR spectroscopy data and an
analysis of distribution of energy among different type of consumers.
