  Shape constraints enable us to reflect prior knowledge in regression
settings. A unimodality constraint, for example, can describe the frequent case
of a first increasing and then decreasing intensity. Yet, data shapes often
exhibit multiple modes. Therefore, we go beyond unimodal regression and propose
modelling multimodality with piecewise unimodal regression or with
deconvolution models based on unimodal peak shapes. Usefulness of unimodal
regression and its multimodal extensions is demonstrated within three
applications areas: marine biology, astroparticle physics and breath gas
analysis. Despite this diversity, valuable results are obtained in each
application. This encourages the use of these methods in other areas as well.
