Robust Uncertainty Quantification and Scalable Computation for Computer Models with Massive Output

Uncertainty quantification (UQ) is both an old and new concept. The current novelty lies in the interactions and synthesis of mathematical models, computer experiments, statistics, field/real experiments, and probability theory, with a particular emphasize on the large-scale simulations by computer models. The challenges not only come from the complication of scientific questions, but also from the size of the information. It is the focus in this thesis to provide statistical models that are scalable to massive data produced in computer experiments and real experiments, through fast and robust statistical inference.

Chapter 2 provides a practical approach for simultaneously emulating/approximating massive number of functions, with the application on hazard quantification of Soufri\`{e}re Hills volcano in Montserrate island. Chapter 3 discusses another problem with massive data, in which the number of observations of a function is large. An exact algorithm that is linear in time is developed for the problem of interpolation of Methylation levels. Chapter 4 and Chapter 5 are both about the robust inference of the models. Chapter 4 provides a new criteria robustness parameter estimation criteria and several ways of inference have been shown to satisfy such criteria. Chapter 5 develops a new prior that satisfies some more criteria and is thus proposed to use in practice.

Biological and ecological mechanisms supporting marine self-governance: The Seri Callo de Hacha Fishery in Mexico

My goal was to describe how biological and ecological factors give shape to fishing practices that can contribute to the successful self-governance of a small-scale fishing system in the Gulf of California, Mexico. The analysis was based on a comparison of the main ecological and biological indicators that fishers claim to use to govern their day-to-day decision making about fishing and data collected in situ. I found that certain indicators allow fishers to learn about differences and characteristics of the resource system and its units. Fishers use such information to guide their day-to-day fishing decisions. More importantly, these decisions appear unable to shape the reproductive viability of the fishery because no indicators were correlated to the reproductive cycle of the target species. As a result, the fishing practices constitute a number of mechanisms that might provide short-term buffering capacity against perturbations or stress factors that otherwise would threaten the overall sustainability and self-governance of the system. The particular biological circumstances that shape the harvesting practices might also act as a precursor of self-governance because they provide fishers with enough incentives to meet the costs of organizing the necessary rule structure that underlies a successful self-governance system.