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Using Bayesian methods for the estimation of uncertainty in complex statistical modelsMargaret R Donald PhD 2008 - 2011 
Faculty Institute for Sustainable Resources/Faculty of Science and Technology Supervisor/s Prof Kerrie Mengersen, Prof Anthony Pettitt Thesis citation This thesis used the simplicity afforded by the Bayesian paradigm, to model uncertainty in complex statistical models for water quality and agriculture.
The first study was a risk assessment of water quality. The assessments were conceived as Bayesian networks with conditional probabilities. Confidence bounds for probabilities were elicited to permit estimation of credible intervals for the outcomes of interest. A further Bayesian network incorporated disparate sets of experimental data underlying risk assessment constants thereby allowing the experimental error from such sources to contribute non-parametrically to uncertainty. The second study analysed crop moisture data across three spatial dimensions and time. A three dimensional conditional autoregressive layered model was developed to describe data for each day, giving a complex set of variance components. In four dimensions, the interactions of time and space were described by repeating the daily model, allowing a realistic model for the complete data. |
