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- All Subjects: BART
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- Creators: Kao, Ming-Hung
- Creators: Zhou, Shuang
- Member of: ASU Electronic Theses and Dissertations
Description
Bayesian Additive Regression Trees (BART) is a non-parametric Bayesian model
that often outperforms other popular predictive models in terms of out-of-sample error. This thesis studies a modified version of BART called Accelerated Bayesian Additive Regression Trees (XBART). The study consists of simulation and real data experiments comparing XBART to other leading algorithms, including BART. The results show that XBART maintains BART’s predictive power while reducing its computation time. The thesis also describes the development of a Python package implementing XBART.
that often outperforms other popular predictive models in terms of out-of-sample error. This thesis studies a modified version of BART called Accelerated Bayesian Additive Regression Trees (XBART). The study consists of simulation and real data experiments comparing XBART to other leading algorithms, including BART. The results show that XBART maintains BART’s predictive power while reducing its computation time. The thesis also describes the development of a Python package implementing XBART.
ContributorsYalov, Saar (Author) / Hahn, P. Richard (Thesis advisor) / McCulloch, Robert (Committee member) / Kao, Ming-Hung (Committee member) / Arizona State University (Publisher)
Created2019
Description
This study concerns optimal designs for experiments where responses consist of both binary and continuous variables. Many experiments in engineering, medical studies, and other fields have such mixed responses. Although in recent decades several statistical methods have been developed for jointly modeling both types of response variables, an effective way to design such experiments remains unclear. To address this void, some useful results are developed to guide the selection of optimal experimental designs in such studies. The results are mainly built upon a powerful tool called the complete class approach and a nonlinear optimization algorithm. The complete class approach was originally developed for a univariate response, but it is extended to the case of bivariate responses of mixed variable types. Consequently, the number of candidate designs are significantly reduced. An optimization algorithm is then applied to efficiently search the small class of candidate designs for the D- and A-optimal designs. Furthermore, the optimality of the obtained designs is verified by the general equivalence theorem. In the first part of the study, the focus is on a simple, first-order model. The study is expanded to a model with a quadratic polynomial predictor. The obtained designs can help to render a precise statistical inference in practice or serve as a benchmark for evaluating the quality of other designs.
ContributorsKim, Soohyun (Author) / Kao, Ming-Hung (Thesis advisor) / Dueck, Amylou (Committee member) / Pan, Rong (Committee member) / Reiser, Mark R. (Committee member) / Stufken, John (Committee member) / Arizona State University (Publisher)
Created2017
Description
This dissertation centers on Bayesian Additive Regression Trees (BART) and Accelerated BART (XBART) and presents a series of models that tackle extrapolation, classification, and causal inference challenges. To improve extrapolation in tree-based models, I propose a method called local Gaussian Process (GP) that combines Gaussian process regression with trained BART trees. This allows for extrapolation based on the most relevant data points and covariate variables determined by the trees' structure. The local GP technique is extended to the Bayesian causal forest (BCF) models to address the positivity violation issue in causal inference. Additionally, I introduce the LongBet model to estimate time-varying, heterogeneous treatment effects in panel data. Furthermore, I present a Poisson-based model, with a modified likelihood for XBART for the multi-class classification problem.
ContributorsWang, Meijia (Author) / Hahn, Paul (Thesis advisor) / He, Jingyu (Committee member) / Lan, Shiwei (Committee member) / McCulloch, Robert (Committee member) / Zhou, Shuang (Committee member) / Arizona State University (Publisher)
Created2024
Description
Bivariate responses that comprise mixtures of binary and continuous variables are common in medical, engineering, and other scientific fields. There exist many works concerning the analysis of such mixed data. However, the research on optimal designs for this type of experiments is still scarce. The joint mixed responses model that is considered here involves a mixture of ordinary linear models for the continuous response and a generalized linear model for the binary response. Using the complete class approach, tighter upper bounds on the number of support points required for finding locally optimal designs are derived for the mixed responses models studied in this work.
In the first part of this dissertation, a theoretical result was developed to facilitate the search of locally symmetric optimal designs for mixed responses models with one continuous covariate. Then, the study was extended to mixed responses models that include group effects. Two types of mixed responses models with group effects were investigated. The first type includes models having no common parameters across subject group, and the second type of models allows some common parameters (e.g., a common slope) across groups. In addition to complete class results, an efficient algorithm (PSO-FM) was proposed to search for the A- and D-optimal designs. Finally, the first-order mixed responses model is extended to a type of a quadratic mixed responses model with a quadratic polynomial predictor placed in its linear model.
In the first part of this dissertation, a theoretical result was developed to facilitate the search of locally symmetric optimal designs for mixed responses models with one continuous covariate. Then, the study was extended to mixed responses models that include group effects. Two types of mixed responses models with group effects were investigated. The first type includes models having no common parameters across subject group, and the second type of models allows some common parameters (e.g., a common slope) across groups. In addition to complete class results, an efficient algorithm (PSO-FM) was proposed to search for the A- and D-optimal designs. Finally, the first-order mixed responses model is extended to a type of a quadratic mixed responses model with a quadratic polynomial predictor placed in its linear model.
ContributorsKhogeer, Hazar Abdulrahman (Author) / Kao, Ming-Hung (Thesis advisor) / Stufken, John (Committee member) / Reiser, Mark R. (Committee member) / Zheng, Yi (Committee member) / Cheng, Dan (Committee member) / Arizona State University (Publisher)
Created2020
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
Geographically Weighted Regression (GWR) has been broadly used in various fields to
model spatially non-stationary relationships. Classic GWR is considered as a single-scale model that is based on one bandwidth parameter which controls the amount of distance-decay in weighting neighboring data around each location. The single bandwidth in GWR assumes that processes (relationships between the response variable and the predictor variables) all operate at the same scale. However, this posits a limitation in modeling potentially multi-scale processes which are more often seen in the real world. For example, the measured ambient temperature of a location is affected by the built environment, regional weather and global warming, all of which operate at different scales. A recent advancement to GWR termed Multiscale GWR (MGWR) removes the single bandwidth assumption and allows the bandwidths for each covariate to vary. This results in each parameter surface being allowed to have a different degree of spatial variation, reflecting variation across covariate-specific processes. In this way, MGWR has the capability to differentiate local, regional and global processes by using varying bandwidths for covariates. Additionally, bandwidths in MGWR become explicit indicators of the scale at various processes operate. The proposed dissertation covers three perspectives centering on MGWR: Computation; Inference; and Application. The first component focuses on addressing computational issues in MGWR to allow MGWR models to be calibrated more efficiently and to be applied on large datasets. The second component aims to statistically differentiate the spatial scales at which different processes operate by quantifying the uncertainty associated with each bandwidth obtained from MGWR. In the third component, an empirical study will be conducted to model the changing relationships between county-level socio-economic factors and voter preferences in the 2008-2016 United States presidential elections using MGWR.
model spatially non-stationary relationships. Classic GWR is considered as a single-scale model that is based on one bandwidth parameter which controls the amount of distance-decay in weighting neighboring data around each location. The single bandwidth in GWR assumes that processes (relationships between the response variable and the predictor variables) all operate at the same scale. However, this posits a limitation in modeling potentially multi-scale processes which are more often seen in the real world. For example, the measured ambient temperature of a location is affected by the built environment, regional weather and global warming, all of which operate at different scales. A recent advancement to GWR termed Multiscale GWR (MGWR) removes the single bandwidth assumption and allows the bandwidths for each covariate to vary. This results in each parameter surface being allowed to have a different degree of spatial variation, reflecting variation across covariate-specific processes. In this way, MGWR has the capability to differentiate local, regional and global processes by using varying bandwidths for covariates. Additionally, bandwidths in MGWR become explicit indicators of the scale at various processes operate. The proposed dissertation covers three perspectives centering on MGWR: Computation; Inference; and Application. The first component focuses on addressing computational issues in MGWR to allow MGWR models to be calibrated more efficiently and to be applied on large datasets. The second component aims to statistically differentiate the spatial scales at which different processes operate by quantifying the uncertainty associated with each bandwidth obtained from MGWR. In the third component, an empirical study will be conducted to model the changing relationships between county-level socio-economic factors and voter preferences in the 2008-2016 United States presidential elections using MGWR.
ContributorsLi, Ziqi (Author) / Fotheringham, A. Stewart (Thesis advisor) / Goodchild, Michael F. (Committee member) / Li, Wenwen (Committee member) / Arizona State University (Publisher)
Created2020