Modeling Probability Density Functions as Data Objects

Recent developments in the probabilistic and statistical analysis of probability density functions are reviewed. Density functions are treated as data objects for which suitable notions of the center of distribution and variability are discussed. Special attention is given to nonlinear methods that respect the constraints density functions must obey. Regression, time series and spatial models are discussed. The exposition is illustrated with data examples. A supplementary vignette contains expanded versions of data analyses with accompanying codes.