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Regular vine copulas can describe a wider array of dependency patterns than the multivariate Gaussian copula or the multivariate Student's t copula. This paper presents two contributions related to model selection of regular vine copulas. First, our pair copula family selection procedure extends existing Bayesian family selection methods by allowing pair families to be chosen from an arbitrary set of candidate families. Second, our method represents the first Bayesian model selection approach to include the regular vine density construction in its scope of inference. The merits of our approach are established in a simulation study that benchmarks against methods suggested in current literature. A real data example about forecasting of portfolio asset returns for risk measurement and investment allocation illustrates the viability and relevance of the proposed scheme.Comment: Published at http://dx.doi.org/10.1214/14-BA930 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/

Context Scientists face several theoretical and methodological challenges in appropriately describing fundamental wildlife-habitat relationships in models. The spatial scales of habitat relationships are often unknown, and are expected to follow a multi-scale hierarchy. Typical frequentist or information theoretic approaches often suffer under collinearity in multiscale studies, fail to converge when models are complex or represent an intractable computational burden when candidate model sets are large. Objectives Our objective was to implement an automated, Bayesian method for inference on the spatial scales of habitat variables that best predict animal abundance. Methods We introduce Bayesian latent indicator scale selection (BLISS), a Bayesian method to select spatial scales of predictors using latent scale indicator variables that are estimated with reversible-jump Markov chain Monte Carlo sampling. BLISS does not suffer from collinearity, and substantially reduces computation time of studies. We present a simulation study to validate our method and apply our method to a case-study of land cover predictors for ring-necked pheasant (Phasianus colchicus) abundance in Nebraska, USA. Results Our method returns accurate descriptions of the explanatory power of multiple spatial scales, and unbiased and precise parameter estimates under commonly encountered data limitations including spatial scale autocorrelation, effect size, and sample size. BLISS outperforms commonly used model selection methods including stepwise and AIC, and reduces runtime by 90%. Conclusions Given the pervasiveness of scale-dependency in ecology, and the implications of mismatches between the scales of analyses and ecological processes, identifying the spatial scales over which species are integrating habitat information is an important step in understanding species-habitat relationships. BLISS is a widely applicable method for identifying important spatial scales, propagating scale uncertainty, and testing hypotheses of scaling relationships.

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