@article{SchuettHarmelingMackeetal.2016,
  author    = {Sch{\"u}tt, Heiko Herbert and Harmeling, Stefan and Macke, Jakob H. and Wichmann, Felix A.},
  title     = {Painfree and accurate Bayesian estimation of psychometric functions for (potentially) overdispersed data},
  series = {Vision research : an international journal for functional aspects of vision.},
  volume    = {122},
  journal   = {Vision research : an international journal for functional aspects of vision.},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0042-6989},
  doi       = {10.1016/j.visres.2016.02.002},
  pages     = {105 -- 123},
  year      = {2016},
  abstract  = {The psychometric function describes how an experimental variable, such as stimulus strength, influences the behaviour of an observer. Estimation of psychometric functions from experimental data plays a central role in fields such as psychophysics, experimental psychology and in the behavioural neurosciences. Experimental data may exhibit substantial overdispersion, which may result from non-stationarity in the behaviour of observers. Here we extend the standard binomial model which is typically used for psychometric function estimation to a beta-binomial model. We show that the use of the beta-binomial model makes it possible to determine accurate credible intervals even in data which exhibit substantial overdispersion. This goes beyond classical measures for overdispersion goodness-of-fit which can detect overdispersion but provide no method to do correct inference for overdispersed data. We use Bayesian inference methods for estimating the posterior distribution of the parameters of the psychometric function. Unlike previous Bayesian psychometric inference methods our software implementation-psignifit 4 performs numerical integration of the posterior within automatically determined bounds. This avoids the use of Markov chain Monte Carlo (MCMC) methods typically requiring expert knowledge. Extensive numerical tests show the validity of the approach and we discuss implications of overdispersion for experimental design. A comprehensive MATLAB toolbox implementing the method is freely available; a python implementation providing the basic capabilities is also available. (C) 2016 The Authors. Published by Elsevier Ltd.},
  language  = {en}
}
@article{HaeringRegerEwaldetal.2013,
  author    = {H{\"a}ring, Tim and Reger, Birgit and Ewald, J{\"o}rg and Hothorn, Torsten and Schr{\"o}der-Esselbach, Boris},
  title     = {Predicting Ellenberg's soil moisture indicator value in the Bavarian Alps using additive georegression},
  series = {Applied vegetation science : official organ of the International Association for Vegetation Science},
  volume    = {16},
  journal   = {Applied vegetation science : official organ of the International Association for Vegetation Science},
  number    = {1},
  publisher = {Wiley-Blackwell},
  address   = {Hoboken},
  issn      = {1402-2001},
  doi       = {10.1111/j.1654-109X.2012.01210.x},
  pages     = {110 -- 121},
  year      = {2013},
  abstract  = {Questions Can forest site characteristics be used to predict Ellenberg indicator values for soil moisture? Which is the best averaged mean value for modelling? Does the distribution of soil moisture depend on spatial information? Location Bavarian Alps, Germany. Methods We used topographic, climatic and edaphic variables to model the mean soil moisture value as found on 1505 forest plots from the database WINALPecobase. All predictor variables were taken from area-wide geodata layers so that the model can be applied to some 250 000 ha of forest in the target region. We adopted methods developed in species distribution modelling to regionalize Ellenberg indicator values. Therefore, we use the additive georegression framework for spatial prediction of Ellenberg values with the R-library mboost, which is a feasible way to consider environmental effects, spatial autocorrelation, predictor interactions and non-stationarity simultaneously in our data. The framework is much more flexible than established statistical and machine-learning models in species distribution modelling. We estimated five different mboost models reflecting different model structures on 50 bootstrap samples in each case. Results Median R2 values calculated on independent test samples ranged from 0.28 to 0.45. Our results show a significant influence of interactions and non-stationarity in addition to environmental covariates. Unweighted mean indicator values can be modelled better than abundance-weighted values, and the consideration of bryophytes did not improve model performance. Partial response curves indicate meaningful dependencies between moisture indicator values and environmental covariates. However, mean indicator values <4.5 and >6.0 could not be modelled correctly, since they were poorly represented in our calibration sample. The final map represents high-resolution information of site hydrological conditions. Conclusions Indicator values offer an effect-oriented alternative to physically-based hydrological models to predict water-related site conditions, even at landscape scale. The presented approach is applicable to all kinds of Ellenberg indicator values. Therefore, it is a significant step towards a new generation of models of forest site types and potential natural vegetation.},
  language  = {en}
}