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- All Subjects: Environmental science
- All Subjects: spatial statistics
- Creators: Saul, Steven
- Status: Published
Description
Spatial regression is one of the central topics in spatial statistics. Based on the goals, interpretation or prediction, spatial regression models can be classified into two categories, linear mixed regression models and nonlinear regression models. This dissertation explored these models and their real world applications. New methods and models were proposed to overcome the challenges in practice. There are three major parts in the dissertation.
In the first part, nonlinear regression models were embedded into a multistage workflow to predict the spatial abundance of reef fish species in the Gulf of Mexico. There were two challenges, zero-inflated data and out of sample prediction. The methods and models in the workflow could effectively handle the zero-inflated sampling data without strong assumptions. Three strategies were proposed to solve the out of sample prediction problem. The results and discussions showed that the nonlinear prediction had the advantages of high accuracy, low bias and well-performed in multi-resolution.
In the second part, a two-stage spatial regression model was proposed for analyzing soil carbon stock (SOC) data. In the first stage, there was a spatial linear mixed model that captured the linear and stationary effects. In the second stage, a generalized additive model was used to explain the nonlinear and nonstationary effects. The results illustrated that the two-stage model had good interpretability in understanding the effect of covariates, meanwhile, it kept high prediction accuracy which is competitive to the popular machine learning models, like, random forest, xgboost and support vector machine.
A new nonlinear regression model, Gaussian process BART (Bayesian additive regression tree), was proposed in the third part. Combining advantages in both BART and Gaussian process, the model could capture the nonlinear effects of both observed and latent covariates. To develop the model, first, the traditional BART was generalized to accommodate correlated errors. Then, the failure of likelihood based Markov chain Monte Carlo (MCMC) in parameter estimating was discussed. Based on the idea of analysis of variation, back comparing and tuning range, were proposed to tackle this failure. Finally, effectiveness of the new model was examined by experiments on both simulation and real data.
In the first part, nonlinear regression models were embedded into a multistage workflow to predict the spatial abundance of reef fish species in the Gulf of Mexico. There were two challenges, zero-inflated data and out of sample prediction. The methods and models in the workflow could effectively handle the zero-inflated sampling data without strong assumptions. Three strategies were proposed to solve the out of sample prediction problem. The results and discussions showed that the nonlinear prediction had the advantages of high accuracy, low bias and well-performed in multi-resolution.
In the second part, a two-stage spatial regression model was proposed for analyzing soil carbon stock (SOC) data. In the first stage, there was a spatial linear mixed model that captured the linear and stationary effects. In the second stage, a generalized additive model was used to explain the nonlinear and nonstationary effects. The results illustrated that the two-stage model had good interpretability in understanding the effect of covariates, meanwhile, it kept high prediction accuracy which is competitive to the popular machine learning models, like, random forest, xgboost and support vector machine.
A new nonlinear regression model, Gaussian process BART (Bayesian additive regression tree), was proposed in the third part. Combining advantages in both BART and Gaussian process, the model could capture the nonlinear effects of both observed and latent covariates. To develop the model, first, the traditional BART was generalized to accommodate correlated errors. Then, the failure of likelihood based Markov chain Monte Carlo (MCMC) in parameter estimating was discussed. Based on the idea of analysis of variation, back comparing and tuning range, were proposed to tackle this failure. Finally, effectiveness of the new model was examined by experiments on both simulation and real data.
ContributorsLu, Xuetao (Author) / McCulloch, Robert (Thesis advisor) / Hahn, Paul (Committee member) / Lan, Shiwei (Committee member) / Zhou, Shuang (Committee member) / Saul, Steven (Committee member) / Arizona State University (Publisher)
Created2020
Description
Marine ecosystems are currently being impacted by various threats; however, quantification of the impacts of known threats and the population status of species are often conducted at different scales, depending upon stakeholder needs. Global-scale species assessments can mask the impact of local or regional threats within the context of global conservation priorities even as conservation policies are generally implemented at the local or regional scale. This work aims to identify the regional threats currently impacting species present within the Gulf of Mexico as well as the current polices addressing those threats. Species currently impacted by threats were used to build an ecosystem model to estimate food web dynamics in the Gulf of Mexico. This model is the first of its kind to incorporate data from more than 1500 species occurring in the Gulf including all marine bony shorefishes, marine reptiles, complete clades of select marine invertebrates, marine birds, marine mammals, and chondrichthyans. Comprehensive analyses of these groups are important for an improved understanding of the functioning of the Gulf of Mexico food web and the impact of identified threats on food web dynamics. The identification of current threats and food web dynamics will help to inform conservation policy moving forward. Properly framed conservation efforts are more likely to be widely accepted and successful when there is an improved understanding on how policies can impact stakeholders both economically and through changing practices. Finally, an investigation of the legal frameworks currently recognized in the Gulf of Mexico was done to build an example tri-national framework between the United States, Mexico, and Cuba focusing on current conservation gaps allowing for specific regional conservation concerns to be addressed.
ContributorsStrongin, Kyle (Author) / Polidoro, Beth (Thesis advisor) / Saul, Steven (Committee member) / Gerber, Leah (Committee member) / Arizona State University (Publisher)
Created2021