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Knowing whether, and to what extent, populations are regulated by density‐dependent factors is important both in its own right and when developing management strategies for wildlife species. However, available tests for density dependence are typically sensitive to sampling errors in the data. By using a state‐space modeling approach, incorporating both an ecological process model and an observation model, it is possible to account for both measurement and process error. Here we focus on the detection and estimation of direct density dependence in two species of North American ducks: the Mallard (Anas platyrhynchos) and the Canvasback (Aythya valisineria). Yearly aerial counts on the major breeding grounds of ducks in North America provide estimates of abundances as well as standard errors of these estimates for both species. Including the number of ponds as a covariate, we demonstrate evidence for density dependence in prairie areas for both species. The appropriateness of the applied state‐space method is validated through a simulation study.
Statistical flood frequency analysis is commonly performed based on a set of annual maximum discharge values which are derived from stage measurements via a stage‐discharge rating curve model. Such design flood estimation techniques often ignore the uncertainty in the underlying rating curve model. Using data from eight gauging stations in Norway, we investigate the effect of curve and sample uncertainty on design flood estimation by combining results from a Bayesian multisegment rating curve model and a Bayesian flood frequency analysis. We find that sample uncertainty is the main contributor to the design flood estimation uncertainty. However, under extrapolation of the rating curve, the uncertainty bounds for both the rating curve model and the flood frequency analysis are highly skewed and ignoring these features may underestimate the potential risk of flooding. We expect this effect to be even more pronounced in arid and semiarid climates with a higher variability in floods.
The present work focuses on extensions of the posterior predictive p-value (ppp-value) for models with hierarchical structure, designed for testing assumptions made on underlying processes. The ppp-values are popular as tools for model criticism, yet their lack of a common interpretation limit their practical use. We discuss different extensions of ppp-values to hierarchical models, allowing for discrepancy measures that can be used for checking properties of the model at all stages. Through analytical derivations and simulation studies on simple models, we show that similar to the standard ppp-values, these extensions are typically far from uniformly distributed under the model assumptions and can give poor power in a hypothesis testing framework. We propose a calibration of the p-values, making the resulting calibrated p-values uniformly distributed under the model conditions. Illustrations are made through a real example of multinomial regression to age distributions of fish.
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