@phdthesis{Cecchini2019,
  author    = {Cecchini, Gloria},
  title     = {Improving network inference by overcoming statistical limitations},
  doi       = {10.25932/publishup-42670},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-426705},
  school      = {Universit{\"a}t Potsdam},
  pages     = {124},
  year      = {2019},
  abstract  = {A reliable inference of networks from data is of key interest in many scientific fields. Several methods have been suggested in the literature to reliably determine links in a network. These techniques rely on statistical methods, typically controlling the number of false positive links, but not considering false negative links. In this thesis new methodologies to improve network inference are suggested. Initial analyses demonstrate the impact of falsepositive and false negative conclusions about the presence or absence of links on the resulting inferred network. Consequently, revealing the importance of making well-considered choices leads to suggest new approaches to enhance existing network reconstruction methods. A simulation study, presented in Chapter 3, shows that different values to balance false positive and false negative conclusions about links should be used in order to reliably estimate network characteristics. The existence of type I and type II errors in the reconstructed network, also called biased network, is accepted. Consequently, an analytic method that describes the influence of these two errors on the network structure is explored. As a result of this analysis, an analytic formula of the density of the biased vertex degree distribution is found (Chapter 4). In the inverse problem, the vertex degree distribution of the true underlying network is analytically reconstructed, assuming the probabilities of type I and type II errors. Chapters 4-5 show that the method is robust to incorrect estimates of α and β within reasonable limits. In Chapter 6, an iterative procedure to enhance this method is presented in the case of large errors on the estimates of α and β. The investigations presented so far focus on the influence of false positive and false negative links on the network characteristics. In Chapter 7, the analysis is reversed - the study focuses on the influence of network characteristics on the probability of type I and type II errors, in the case of networks of coupled oscillators. The probabilities of α and β are influenced by the shortest path length and the detour degree, respectively. These results have been used to improve the network reconstruction, when the true underlying network is not known a priori, introducing a novel and advanced concept of threshold.},
  language  = {en}
}
@article{MauerbergerSchannerKorteetal.2020,
  author    = {Mauerberger, Stefan and Schanner, Maximilian Arthus and Korte, Monika and Holschneider, Matthias},
  title     = {Correlation based snapshot models of the archeomagnetic field},
  series = {Geophysical journal international},
  volume    = {223},
  journal   = {Geophysical journal international},
  number    = {1},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0956-540X},
  doi       = {10.1093/gji/ggaa336},
  pages     = {648 -- 665},
  year      = {2020},
  abstract  = {For the time stationary global geomagnetic field, a new modelling concept is presented. A Bayesian non-parametric approach provides realistic location dependent uncertainty estimates. Modelling related variabilities are dealt with systematically by making little subjective apriori assumptions. Rather than parametrizing the model by Gauss coefficients, a functional analytic approach is applied. The geomagnetic potential is assumed a Gaussian process to describe a distribution over functions. Apriori correlations are given by an explicit kernel function with non-informative dipole contribution. A refined modelling strategy is proposed that accommodates non-linearities of archeomagnetic observables: First, a rough field estimate is obtained considering only sites that provide full field vector records. Subsequently, this estimate supports the linearization that incorporates the remaining incomplete records. The comparison of results for the archeomagnetic field over the past 1000 yr is in general agreement with previous models while improved model uncertainty estimates are provided.},
  language  = {en}
}
@article{Buerger2018,
  author    = {B{\"u}rger, Gerd},
  title     = {A counterexample to decomposing climate shifts and trends by weather types},
  series = {International Journal of Climatology},
  volume    = {38},
  journal   = {International Journal of Climatology},
  number    = {9},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {0899-8418},
  doi       = {10.1002/joc.5519},
  pages     = {3732 -- 3735},
  year      = {2018},
  abstract  = {The literature contains a sizable number of publications where weather types are used to decompose climate shifts or trends into contributions of frequency and mean of those types. They are all based on the product rule, that is, a transformation of a product of sums into a sum of products, the latter providing the decomposition. While there is nothing to argue about the transformation itself, its interpretation as a climate shift or trend decomposition is bound to fail. While the case of a climate shift may be viewed as an incomplete description of a more complex behaviour, trend decomposition indeed produces bogus trends, as demonstrated by a synthetic counterexample with well-defined trends in type frequency and mean. Consequently, decompositions based on that transformation, be it for climate shifts or trends, must not be used.},
  language  = {en}
}