Some distance bounds of branching processes and their diffusion limits

We compute exact values respectively bounds of "distances" - in the sense of (transforms of) power divergences and relative entropy - between two discrete-time Galton-Watson branching processes with immigration GWI for which the offspring as well as the immigration is arbitrarily Poisson-distributed (leading to arbitrary type of criticality). Implications for asymptotic distinguishability behaviour in terms of contiguity and entire separation of the involved GWI are given, too. Furthermore, we determine the corresponding limit quantities for the context in which the two GWI converge to Feller-type branching diffusion processes, as the time-lags between observations tend to zero. Some applications to (static random environment like) Bayesian decision making and Neyman-Pearson testing are presented as well.Comment: 45 page

Robust Procedures for Estimating and Testing in the Framework of Divergence Measures

The scope of the contributions to this book will be to present new and original research papers based on MPHIE, MHD, and MDPDE, as well as test statistics based on these estimators from a theoretical and applied point of view in different statistical problems with special emphasis on robustness. Manuscripts given solutions to different statistical problems as model selection criteria based on divergence measures or in statistics for high-dimensional data with divergence measures as loss function are considered. Reviews making emphasis in the most recent state-of-the art in relation to the solution of statistical problems base on divergence measures are also presented

Remote Sensing Data Assimilation in Dynamic Crop Models Using Particle Swarm Optimization

A growing world population, increasing prosperity in emerging countries, and shifts in energy and food demands necessitate a continuous increase in global agricultural production. Simultaneously, risks of extreme weather events and a slowing productivity growth in recent years has caused concerns about meeting the demands in the future. Crop monitoring and timely yield predictions are an important tool to mitigate risk and ensure food security. A common approach is to combine the temporal simulation of dynamic crop models with a geospatial component by assimilating remote sensing data. To ensure reliable assimilation, handling of uncertainties in both models and the assimilated input data is crucial. Here, we present a new approach for data assimilation using particle swarm optimization (PSO) in combination with statistical distance metrics that allow for flexible handling of model and input uncertainties. We explored the potential of the newly proposed method in a case study by assimilating canopy cover (CC) information, obtained from Sentinel-2 data, into the AquaCrop-OS model to improve winter wheat yield estimation on the pixel- and field-level and compared the performance with two other methods (simple updating and extended Kalman filter). Our results indicate that the performance of the new method is superior to simple updating and similar or better than the extended Kalman filter updating. Furthermore, it was particularly successful in reducing bias in yield estimation

Unsupervised Image Regression for Heterogeneous Change Detection

Change detection (CD) in heterogeneous multitemporal satellite images is an emerging and challenging topic in remote sensing. In particular, one of the main challenges is to tackle the problem in an unsupervised manner. In this paper, we propose an unsupervised framework for bitemporal heterogeneous CD based on the comparison of affinity matrices and image regression. First, our method quantifies the similarity of affinity matrices computed from colocated image patches in the two images. This is done to automatically identify pixels that are likely to be unchanged. With the identified pixels as pseudotraining data, we learn a transformation to map the first image to the domain of the other image and vice versa. Four regression methods are selected to carry out the transformation: Gaussian process regression, support vector regression, random forest regression (RFR), and a recently proposed kernel regression method called homogeneous pixel transformation. To evaluate the potentials and limitations of our framework and also the benefits and disadvantages of each regression method, we perform experiments on two real data sets. The results indicate that the comparison of the affinity matrices can already be considered a CD method by itself. However, image regression is shown to improve the results obtained by the previous step alone and produces accurate CD maps despite of the heterogeneity of the multitemporal input data. Notably, the RFR approach excels by achieving similar accuracy as the other methods, but with a significantly lower computational cost and with fast and robust tuning of hyperparameters