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

Corani, Giorgio and Mignatti, Andrea (2015) Robust Bayesian model averaging for the analysis of presence–absence data. Environmental and Ecological Statistics, 22 (3). pp. 513-534. ISSN 1352-8505

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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.

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