Hierarchical Models for Estimation of Population Parameters

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The Challenge: Much of wildlife research consists of the description of variation in data. Some of the variation results from spatial and temporal change in populations, while some results from biologically irrelevant sampling variation induced by the process of data collection. Distinguishing relevant from irrelevant variation is the first task of statistical analysis, but the job does not end there. Even if the true values of population parameters were known, without the contamination of sampling variation, the investigation of population processes would require an evaluation of pattern among parameters.

The Science: Hierarchical models treat unknown population parameters as random variables, with probability distributions governed by hyperparameters. Knowledge of these stochastic relationships is fundamental to the understanding of demographic processes.  

The analysis of hierarchical models has been facilitated by recent advances in Bayesian analysis, and computationally intensive techniques such as Markov Chain Monte Carlo. This study has been undertaken with the goal of promoting and developing hierarchical modeling solutions for demographic analysis.  

For example, the demographic buffering hypothesis states that natural selection favors low temporal variability in population sensitive demographic parameters. An evaluation of this hypothesis using a 30-year mark-recapture data set for Weddell seals (Leptonychotes weddellii) required estimation not only of survival and recruitment rates, but also estimation of temporal variation and covariation among the rates.

The Future: Model selection and model criticism are important problems in statistical inference, and have been widely studied for simple models.  These problems are more difficult for hierarchical models.  Bayesian p-values and model weighting are tools for these tasks, but there is a need for further development of methods.

Work continues on the development and use of the Bayesian Predictive Information Criterion (BPIC) and a surrogate, the Watanabe/Akaike Information Criterion (WAIC).  These are measures of the predictive ability of models, and are being used to compare  trend models for the North American Breeding Bird Survey.  BPIC is the gold standard, but is enormously computationally intensive, almost prohibitively so, even with parallel processing on fast multi-core computer systems.  Work is in progress on combining the computational efficiencies of WAIC with the superior performance of BPIC.