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We perform a Bayesian analysis on abundance data for ten species of North American duck, using the results to investigate the evidence in favour of biologically motivated hypotheses about the causes and mechanisms of density dependence in these species. We explore the capabilities of our methods to detect density dependent effects, both by simulation and through analyzes of real data. The effect of the prior choice on predictive accuracy is also examined. We conclude that our priors, which are motivated by considering the dynamics of the system of interest, offer clear advances over the priors used by previous authors for the duck data sets. We use this analysis as a motivating example to demonstrate the importance of careful parameter prior selection if we are to perform a balanced model selection procedure. We also present some simple guidelines that can be followed in a wide variety of modelling frameworks where vague parameter prior choice is not a viable option. These will produce parameter priors that not only greatly reduce bias in selecting certain models, but improve the predictive ability of the resulting model-averaged predictor.
Bayesian methods - either based on Bayes Factors or BIC - are now widely used for model selection. One property that might reasonably be demanded of any model selection method is that if a model ${M}_{1}$ is preferred to a model ${M}_{0}$, when these
This document is an invited chapter covering the specificities of ABC model choice, intended for the incoming Handbook of ABC by Sisson, Fan, and Beaumont (2017). Beyond exposing the potential pitfalls of ABC based posterior probabilities, the review
We propose the variable selection procedure incorporating prior constraint information into lasso. The proposed procedure combines the sample and prior information, and selects significant variables for responses in a narrower region where the true p
The standard importance sampling (IS) estimator, generally does not work well in examples involving simultaneous inference on several targets as the importance weights can take arbitrarily large values making the estimator highly unstable. In such si
Two algorithms proposed by Leo Breiman : CART trees (Classification And Regression Trees for) introduced in the first half of the 80s and random forests emerged, meanwhile, in the early 2000s, are the subject of this article. The goal is to provide e