Beyond unimodal regression: modelling multimodality with piecewise unimodal regression or deconvolution models

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.