Eliciting and encoding expert knowledge on variable selection into classical or Bayesian species distribution models

The quality of species distribution models (SDMs) relies to a large degree on the quality of the input data, from bioclimatic indices to environmental and habitat descriptors (Austin, 2002). Recent reviews of SDM techniques, have sought to optimize predictive performance e.g. Elith et al., 2006. In general SDMs employ one of three approaches to variable selection. The simplest approach relies on the expert to select the variables, as in environmental niche models Nix, 1986 or a generalized linear model without variable selection (Miller and Franklin, 2002). A second approach explicitly incorporates variable selection into model fitting, which allows examination of particular combinations of variables. Examples include generalized linear or additive models with variable selection (Hastie et al. 2002); or classification trees with complexity or model based pruning (Breiman et al., 1984, Zeileis, 2008). A third approach uses model averaging, to summarize the overall contribution of a variable, without considering particular combinations. Examples include neural networks, boosted or bagged regression trees and Maximum Entropy as compared in Elith et al. 2006. Typically, users of SDMs will either consider a small number of variable sets, via the first approach, or else supply all of the candidate variables (often numbering more than a hundred) to the second or third approaches. Bayesian SDMs exist, with several methods for eliciting and encoding priors on model parameters (see review in Low Choy et al. 2010). However few methods have been published for informative variable selection; one example is Bayesian trees (O’Leary 2008). Here we report an elicitation protocol that helps makes explicit a priori expert judgements on the quality of candidate variables. This protocol can be flexibly applied to any of the three approaches to variable selection, described above, Bayesian or otherwise. We demonstrate how this information can be obtained then used to guide variable selection in classical or machine learning SDMs, or to define priors within Bayesian SDMs.

Herman Sommerfeld (center) with other reserve soldiers in military uniform Portraits Men

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Herman Sommerfeld (center) with other soldiers in military uniform Portraits Men

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Reproduction of grammar school class portrait including Fred Herz (front center).

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Studio portrait of Dr. Moritz Kroner (center) with two unidentified men in military uniform.

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Historian Herbert Strauss standing in front of an exhibition at the ZFA (Zentrum für Antisemitismusforschung; Center for Research on Antisemitism); Berlin Portraits Men

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Dr. Rainer Erb at the ZFA (Zentrum für Antisemitismusforschung; Center for Research on Antisemitism); Berlin Portraits Men

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Ingeborg Medani seated at her desk at the ZFA (Zentrum für Antisemitismusforschung; Center for Research on Antisemitism); Berlin Portraits Women

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Two unidentified women working in the Library of the ZFA (Zentrum für Antisemitismusforschung; Center for Research on Antisemitism); Berlin Portraits Women

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Exhibition on the history of antisemitism at the ZFA (Zentrum für Antisemitismusforschung; Center for Research on Antisemitism); Berlin.

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Telephone and security pad at the entrance of the ZFA (Zentrum für Antisemitismusforschung; Center for Research on Antisemitism); Berlin.

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Studies of phosphazenes. 28. Reactions of pentachloro- and pentafluoro(triphenylphosphazenyl)cyclotriphosphazenes with sodium methoxide. Mechanistic aspects and their implications for nucleophilic displacement at a tetrahedral phosphorus(V) center

Abstract is not available.

Young Herbert Strauss (center) with four friends seated on a park bench on the Sabbath; Würzburg.

To the right of Herbert Strauss are Anne Chrenbacher and Walther Reis, to his left are Heinz Ostheim and an unidentified woman