Probability-Based Estimation

We develop a theory of estimation when in addition to a sample of $n$ observed outcomes the underlying probabilities of the observed outcomes are known, as is typically the case in the context of numerical simulation modeling, e.g. in epidemiology. For this enriched information framework, we design unbiased and consistent ``probability-based'' estimators whose variance vanish exponentially fast as $n\to\infty$, as compared to the power-law decline of classical estimators' variance.Comment: 5 page

Timing of Transients : Quantifying Reaching Times and Transient Behavior in Complex Systems

The authors thank the anonymous referees for their detailed and constructive feedback. This paper was developed within the scope of the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP. This work was conducted in the framework of PIK’s flagship project on coevolutionary pathways (copan). The authors thank CoNDyNet (FKZ 03SF0472A) for their cooperation. The authors gratefully acknowledge the European Regional Development Fund (ERDF), the German Federal Ministry of Education and Research and the Land Brandenburg for supporting this project by providing resources on the high performance computer system at the Potsdam Institute for Climate Impact Research. The authors thank the developers of the used software: Python[47], Numerical Python[48] and Scientific Python[49]. The authors thank Sabine Auer, Karsten Bolts, Catrin Ciemer, Jonathan Donges, Reik Donner, Jasper Franke, Frank Hellmann, Jakob Kolb, Chiranjit Mitra, Finn Muller-Hansen, Jan Nitzbon, Anton Plietzsch Stefan Ruschel, Tiago Pereira da Silva, Francisco A. Rodrigues, Paul Schultz, and Lyubov Tupikina for helpful discussions and comments.Peer reviewedPublisher PD

Mappings between distance sets or spaces

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