Complex Bayesian models: construction, and sampling strategies

Bayesian models are useful tools for realistically modeling processes occurring in the real world. In particular, we consider models for spatio-temporal data where the response vector is compositional, ie. has components that sum-to-one. A unique multivariate conditional hierarchical model (MVCAR) is proposed. Statistical methods for MVCAR models are well developed and we extend these tools for use with a discrete compositional response. We harness the advantages of an MVCAR model when the response variables of interest are relational, rather than absolute measures. Drawbacks that exist in current modeling approaches for such data are addressed. Following this, we consider the role of sample selection as a way to support, and to improve the robustness, of Bayesian hierarchical models. We develop guidelines for cre- ating ignorable sampling approaches for complex Bayesian models. This is demonstrated through development of approaches appropriate for our MVCAR model. In particular, a response dependent adaptive approach based on exact sample size requirements for multi- nomial data is offered. We initiate a context for considering ‘optimality’ of different sampling methods when the criteria being optimized is a surface, not a scalar. Our optimality evaluation approach is unified with literature about Bayesianly justifiable simulation approaches, including poste- rior predictive checks. An example from Fraser River Sockeye salmon fisheries where compositional data pro- vides information about stock run-timings during spawning migration and motivates this work. Such monitoring data with spatial or temporal components occur in a wide variety of applications. Technologies for both measurement and data storage have improved; data are better and there is more of it. Concurrently, society has become more aware of its important relationship to understanding and managing complex natural systems.