Subset selection in dimension reduction methods

Dimension reduction methods play an important role in multivariate statistical analysis, in particular with high-dimensional data. Linear methods can be seen as a linear mapping from the original feature space to a dimension reduction subspace. The aim is to transform the data so that the essential structure is more easily understood. However, highly correlated variables provide redundant information, whereas some other feature may be irrelevant, and we would like to identify and then discard both of them while pursuing dimension reduction. Here we propose a greedy search algorithm, which avoids the search over all possible subsets, for ranking subsets of variables based on their ability to explain variation in the dimension reduction variates.Dimension reduction methods, Linear mapping, Subset selection, Greedy search

Multivariate emulation of computer simulators: model selection and diagnostics with application to a humanitarian relief model

We present a common framework for Bayesian emulation methodologies for multivariate-output simulators, or computer models, that employ either parametric linear models or nonparametric Gaussian processes. Novel diagnostics suitable for multivariate covariance-separable emulators are developed and techniques to improve the adequacy of an emulator are discussed and implemented. A variety of emulators are compared for a humanitarian relief simulator, modelling aid missions to Sicily after a volcanic eruption and earthquake, and a sensitivity analysis is conducted to determine the sensitivity of the simulator output to changes in the input variables. The results from parametric and nonparametric emulators are compared in terms of prediction accuracy, uncertainty quantification and scientific interpretability

Improving Stock Assessments and Management Advice for Bluefin Tunas and Other Highly Migratory Species

For years bluefin tuna has been the poster child for overfishing and poor management. However, recent improvements in data collection, catch monitoring and international cooperation are providing an opportunity to reverse the perception of a fishery that is doomed to collapse. Stock assessments are conducted routinely to monitor the abundance and productivity of exploited fish stocks so managers can determine how many fish can be sustainably harvested each year. Should a stock be declared overfished or under-going overfishing, the science behind stock assessments also equip managers with the knowledge necessary to make decisions about what short-term and long-term management measures should be taken to help reverse these trends. in that light, the goal of my research has been to use newly available age data to improve the quality and reliability of assessments for Atlantic bluefin tuna by reducing uncertainty about the data and methods used to infer growth and age composition. A secondary goal has been to provide managers with the knowledge necessary to implement effective stock rebuilding programs for Pacific bluefin tuna. Chapter 2 is focused on cohort slicing, a method routinely used in the Atlantic bluefin tuna assessment to estimate catch-at-age from catch-at-size information. This chapter explores how errors in cohort sliced catch-at-age data can bias estimates of total mortality rate derived from catch curve analysis. Recommendations are provided concerning the appropriate mortality estimator and plus group to use depending on the parameters characterizing the stock. Chapter 3 provides updated growth estimates for western Atlantic bluefin tuna, which were adopted in 2017 as the basis for defining growth in the assessment. Chapter 4 provides an overview of the theory behind age-length keys with particular emphasis on the assumptions that govern each method and provides notes of caution concerning their applications to real data. Chapter 5 evaluates through simulation the relative performance of different methods for estimating age composition of western Atlantic bluefin tuna catches and applies the best performing technique, the combined forward-inverse age-length key, to actual western Atlantic bluefin tuna data. Chapter 6 moves over to the Pacific and focuses on evaluating the potential impacts of different minimum size regulations on the stock of Pacific bluefin tuna and explores ways in which to minimize short-term pain to the industry while still achieving long-term yield and conservation goals. Overall, this work has contributed major improvements to the stock assessment process of Atlantic bluefin tuna and implications of this work resonate beyond the bluefin tuna world to other highly migratory species faced with similar problems