  The amount, size, and complexity of astronomical data-sets and databases are
growing rapidly in the last decades, due to new technologies and dedicated
survey telescopes. Besides dealing with poly-structured and complex data,
sparse data has become a field of growing scientific interest. A specific field
of Astroinformatics research is the estimation of redshifts of extra-galactic
sources by using sparse photometric observations. Many techniques have been
developed to produce those estimates with increasing precision. In recent
years, models have been favored which instead of providing a point estimate
only, are able to generate probabilistic density functions (PDFs) in order to
characterize and quantify the uncertainties of their estimates.
  Crucial to the development of those models is a proper, mathematically
principled way to evaluate and characterize their performances, based on
scoring functions as well as on tools for assessing calibration. Still, in
literature inappropriate methods are being used to express the quality of the
estimates that are often not sufficient and can potentially generate misleading
interpretations. In this work we summarize how to correctly evaluate errors and
forecast quality when dealing with PDFs. We describe the use of the
log-likelihood, the continuous ranked probability score (CRPS) and the
probability integral transform (PIT) to characterize the calibration as well as
the sharpness of predicted PDFs. We present what we achieved when using proper
scoring rules to train deep neural networks as well as to evaluate the model
estimates and how this work led from well calibrated redshift estimates to
improvements in probabilistic weather forecasting. The presented work is an
example of interdisciplinarity in data-science and illustrates how methods can
help to bridge gaps between different fields of application.
