Environmental and Ecological Statistics

, Volume 22, Issue 3, pp 513–534 | Cite as

Robust Bayesian model averaging for the analysis of presence–absence data

  • Giorgio Corani
  • Andrea Mignatti


When developing a species distribution model, usually one tests several competing models such as logistic regressions characterized by different sets of covariates. Yet, there is an exponential number of subsets of covariates to choose from. This generates the problem of model uncertainty. Bayesian model averaging (BMA) is a state-of-the-art approach to deal with model uncertainty. BMA weights the inferences of multiple models. However, the results yielded by BMA depend on the prior probability assigned to the models. Credal model averaging (CMA) extends BMA towards robustness. It substitutes the single prior over the models by a set of priors. The CMA inferences (e.g., posterior probability of inclusion of a covariate, coefficient of a covariate, probability of presence) are intervals. The interval shows the sensitivity of the BMA estimate on the prior over the models. CMA detects the prior-dependent instances, namely cases in which the most probable outcome becomes presence or absence depending on the adopted prior over the models. On such prior-dependent instances, BMA behaves almost as a random guesser. The weakness of BMA on the prior-dependent instances is to our knowledge pointed out for the first time in the ecological literature. On the prior-dependent instances CMA avoids random guessing acknowledging undecidability. In this way it stimulates the decision maker to convey further information before taking the decision. We provide thorough experiments on different data sets.


Bayesian model averaging Credal model averaging Imprecise probability Logistic regression Presence–absence Robust Bayesian analysis Species distribution model  



The work has been performed during Andrea Mignatti’s Ph.D., supported by Fondazione Lombardia per l’Ambiente (project SHARE—Stelvio). We are grateful to B.A. Wintle for providing us with the greater glider data set. We thank M. Gatto, R. Casagrandi, V. Brambilla, M. Cividini and F. Mattioli for the help provided in collecting marmot data. We also thank the anonymous reviewers for their valuable suggestions.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Istituto Dalle Molle di studi sull’Intelligenza Artificiale (IDSIA)Scuola universitaria professionale della Svizzera italiana (SUPSI), Università della Svizzera italiana (USI)LuganoSwitzerland
  2. 2.Dipartimento di Elettronica, Informazione e BioingegneriaPolitecnico di MilanoMilanItaly

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