@article{DuttaJonssonVasyuraBathke2021,
  author    = {Dutta, Rishabh and J{\´o}nsson, Sigurj{\´o}n and Vasyura-Bathke, Hannes},
  title     = {Simultaneous Bayesian estimation of non-planar fault geometry and spatially-variable slip},
  series = {JGR / AGU, American Geophysical Union : Solid earth},
  volume    = {126},
  journal   = {JGR / AGU, American Geophysical Union : Solid earth},
  number    = {7},
  publisher = {Wiley},
  address   = {Hoboken, NJ},
  issn      = {2169-9313},
  doi       = {10.1029/2020JB020441},
  pages     = {28},
  year      = {2021},
  abstract  = {Large earthquakes are usually modeled with simple planar fault surfaces or a combination of several planar fault segments. However, in general, earthquakes occur on faults that are non-planar and exhibit significant geometrical variations in both the along-strike and down-dip directions at all spatial scales. Mapping of surface fault ruptures and high-resolution geodetic observations are increasingly revealing complex fault geometries near the surface and accurate locations of aftershocks often indicate geometrical complexities at depth. With better geodetic data and observations of fault ruptures, more details of complex fault geometries can be estimated resulting in more realistic fault models of large earthquakes. To address this topic, we here parametrize non-planar fault geometries with a set of polynomial parameters that allow for both along-strike and down-dip variations in the fault geometry. Our methodology uses Bayesian inference to estimate the non-planar fault parameters from geodetic data, yielding an ensemble of plausible models that characterize the uncertainties of the non-planar fault geometry and the fault slip. The method is demonstrated using synthetic tests considering slip spatially distributed on a single continuous finite non-planar fault surface with varying dip and strike angles both in the down-dip and along-strike directions. The results show that fault-slip estimations can be biased when a simple planar fault geometry is assumed in presence of significant non-planar geometrical variations. Our method can help to model earthquake fault sources in a more realistic way and may be extended to include multiple non-planar fault segments or other geometrical fault complexities.},
  language  = {en}
}
@article{GravesFranzkeWatkinsetal.2017,
  author    = {Graves, Timothy and Franzke, Christian L. E. and Watkins, Nicholas W. and Gramacy, Robert B. and Tindale, Elizabeth},
  title     = {Systematic inference of the long-range dependence and heavy-tail distribution parameters of ARFIMA models},
  series = {Physica : europhysics journal ; A, Statistical mechanics and its applications},
  volume    = {473},
  journal   = {Physica : europhysics journal ; A, Statistical mechanics and its applications},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0378-4371},
  doi       = {10.1016/j.physa.2017.01.028},
  pages     = {60 -- 71},
  year      = {2017},
  language  = {en}
}
@article{KruegelEngbert2014,
  author    = {Kruegel, Andre and Engbert, Ralf},
  title     = {A model of saccadic landing positions in reading under the influence of sensory noise},
  series = {Visual cognition},
  volume    = {22},
  journal   = {Visual cognition},
  number    = {3-4},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1350-6285},
  doi       = {10.1080/13506285.2014.894166},
  pages     = {334 -- 353},
  year      = {2014},
  language  = {en}
}
@phdthesis{Goswami2014,
  author    = {Goswami, Bedartha},
  title     = {Uncertainties in climate data analysis},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-78312},
  school      = {Universit{\"a}t Potsdam},
  year      = {2014},
  abstract  = {Scientific inquiry requires that we formulate not only what we know, but also what we do not know and by how much. In climate data analysis, this involves an accurate specification of measured quantities and a consequent analysis that consciously propagates the measurement errors at each step. The dissertation presents a thorough analytical method to quantify errors of measurement inherent in paleoclimate data. An additional focus are the uncertainties in assessing the coupling between different factors that influence the global mean temperature (GMT). Paleoclimate studies critically rely on `proxy variables' that record climatic signals in natural archives. However, such proxy records inherently involve uncertainties in determining the age of the signal. We present a generic Bayesian approach to analytically determine the proxy record along with its associated uncertainty, resulting in a time-ordered sequence of correlated probability distributions rather than a precise time series. We further develop a recurrence based method to detect dynamical events from the proxy probability distributions. The methods are validated with synthetic examples and demonstrated with real-world proxy records. The proxy estimation step reveals the interrelations between proxy variability and uncertainty. The recurrence analysis of the East Asian Summer Monsoon during the last 9000 years confirms the well-known `dry' events at 8200 and 4400 BP, plus an additional significantly dry event at 6900 BP. We also analyze the network of dependencies surrounding GMT. We find an intricate, directed network with multiple links between the different factors at multiple time delays. We further uncover a significant feedback from the GMT to the El Ni{\~n}o Southern Oscillation at quasi-biennial timescales. The analysis highlights the need of a more nuanced formulation of influences between different climatic factors, as well as the limitations in trying to estimate such dependencies.},
  language  = {en}
}