Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Heikki Haario, LUT University (Technische Universität Lappeenranta), Finland
We discuss methods for creating Gaussian likelihoods for data that does not directly follow any known statistics. Obvious summary statistics are available, such as averages, but they turn out to lose too much information. The challenge thus is to find summaries that are both Gaussian and sensitive with respect to the parameters of the system, i.e., changes in the geometry of the underlying attractor. We discuss such approaches starting from fractal dimension concepts. The starting point is to consider Ecdf's of the distances between point clouds of observations, and use resampling to estimate their mean and covariance. Examples are provided by chaotic and/or stochastic signals, as well random Turing patterns.
invited by Jana de Wiljes