title: Quantitative approaches for environmental decision making
Creators: name: Shobeirinejad, Ameneh
Publisher: name: Griffith University
Year: 2017
Subjects: subject: Quantitative approaches
subject: Environmental decision making
subject: Bayesian approaches

description: Ecologists and environmental managers regularly need to make decisions about restoration and management with limited information and uncertainty about the outcomes of system interventions. Uncertainty is an inevitable component of environmental management and decision making (as well as other complex systems’ management); however, the significance of environmental problems necessitates the effort to quantify and, where possible, minimise the uncertainty around the outputs of models of a given system. Uncertainty about the model output stems from the uncertainty about the model input (arising from different sources) and the model structure. The latter is the more complex of the two and as such challenging to address. There are a range of quantitative methods available to assist with environmental management and decision making. However, while finding one specific model to represent a system effectively is an ideal goal, the selection of the most suitable model among those available is a challenging task for the modeller. Model selection includes at least two aspects, the selection of appropriate variables and an appropriate model structure. Model structure describes the nature of the mathematical representation of the cause and effect relationships that are quantified by the model. Many approaches for variable selection already exist; however, methods to guide the quantitative selection of an appropriate model structure are not so well developed. Model structure selection is an important step in modelling, which needs not only to include the essential variables and processes of the system, but also to avoid unnecessary complexity that doesn’t improve the modelling results. Selecting an appropriate model structure involves several related steps. One step is to determine the possible nature of the cause and effect relationships among the variables. A second step is to investigate carefully the amount and the quality of the available information, along with evaluating the uncertainty about the conditions, the variables and the modelling parameters, and then selecting one out of many model structures. For example, the modeller may decide to use deterministic models, or to embody some stochastic components in the model and assign some probability to the occurrence of some random variables. For the latter, they may decide to use a statistical model or other probabilistic models, such as Bayesian networks. They may decide to represent the whole system with one model of the system, or may choose to break the large-scale system down into simpler ones and use different models to represent the more clear cause and effect relationships among variables. Among the many aspects of model structure for a modeller to select, there is the choice between a single-level and a multi-level model structure. Single-level models represent the relationships between variables with fixed coefficients, and in case the data are grouped, ignore the group differences. Conversely, hierarchical models consider the relationships within and between levels of grouped data and can account for the variation between groups. Hierarchical models can include varying coefficients to quantify how relationships between variables at one level may depend on variables at other levels. The complexity and heterogeneity of environmental and ecological systems can benefit from the use of hierarchical models to accommodate more complexity and embrace different principles that might apply at different scales. However, compared to single-level models, hierarchical models are considerably more complex and more difficult to implement. Therefore, there is a strong need to understand the conditions where the additional work of fitting a hierarchical model is necessary. In this research, I aimed to identify the statistical conditions under which hierarchical models provide a better fit to complex data than single level models. This involved the analysis of an empirical ecological dataset in tandem with a large simulation study of 70,000 datasets. The simulation study provided a way to analyse a large range of datasets with known structure, uncertainty and relationships among the variables, while the empirical study provided an avenue to test the approach in a real setting with noisy data. For the simulation study, I set both single-level and hierarchical models’ structures as Poisson regression (due to the importance of this distribution in a large number of ecological studies) in a Bayesian framework. The Bayesian framework is a flexible approach that is used increasingly to quantify environmental and ecological processes, and guide decision making. A key feature of Bayesian approaches is the capacity to quantify uncertainty at all levels of the model and propagate that uncertainty through to the response or outcome variable. This ensures that uncertainty around predictions from the model, be they ecological responses to natural disturbances or management interventions, is naturally included in the model output. Moreover, Hierarchical Bayesian models offer great promise in quantifying multiscale processes and developing complex probabilistic models that reflect underlying ecological processes. The results of the simulation study identified which of the 70,000 datasets where a hierarchical model fit better than a single-level model. Based on the findings, I developed a statistical tool for model-structure selection that can be efficiently applied to a set of data, and recommend a modelstructure with an accompanying reliability of recommendation. This tool provides a quantitative approach to inform users when the additional effort of hierarchical modelling would provide a better model fit and when the simpler single level model structures are appropriate. To demonstrate the applicability of the proposed model-structure selection tool, I applied the proposed tool to three empirical ecological datasets. I also developed both single-level and hierarchical models on these datasets and compared standard goodness fit metrics to the recommendation from my proposed tool. For all datasets, the proposed tool recommended, with a very high reliability of recommendation, the same model-structure selected as the better fit by modelling results.