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Description
In this work, I present a Bayesian inference computational framework for the analysis of widefield microscopy data that addresses three challenges: (1) counting and localizing stationary fluorescent molecules; (2) inferring a spatially-dependent effective fluorescence profile that describes the spatially-varying rate at which fluorescent molecules emit subsequently-detected photons (due to different illumination intensities or different local environments); and (3) inferring the camera gain. My general theoretical framework utilizes the Bayesian nonparametric Gaussian and beta-Bernoulli processes with a Markov chain Monte Carlo sampling scheme, which I further specify and implement for Total Internal Reflection Fluorescence (TIRF) microscopy data, benchmarking the method on synthetic data. These three frameworks are self-contained, and can be used concurrently so that the fluorescence profile and emitter locations are both considered unknown and, under some conditions, learned simultaneously. The framework I present is flexible and may be adapted to accommodate the inference of other parameters, such as emission photophysical kinetics and the trajectories of moving molecules. My TIRF-specific implementation may find use in the study of structures on cell membranes, or in studying local sample properties that affect fluorescent molecule photon emission rates.
ContributorsWallgren, Ross (Author) / Presse, Steve (Thesis advisor) / Armbruster, Hans (Thesis advisor) / McCulloch, Robert (Committee member) / Arizona State University (Publisher)
Created2019
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
Optimal experimental design for generalized linear models is often done using a pseudo-Bayesian approach that integrates the design criterion across a prior distribution on the parameter values. This approach ignores the lack of utility of certain models contained in the prior, and a case is demonstrated where the heavy focus on such hopeless models results in a design with poor performance and with wild swings in coverage probabilities for Wald-type confidence intervals. Design construction using a utility-based approach is shown to result in much more stable coverage probabilities in the area of greatest concern.
The pseudo-Bayesian approach can be applied to the problem of optimal design construction under dependent observations. Often, correlation between observations exists due to restrictions on randomization. Several techniques for optimal design construction are proposed in the case of the conditional response distribution being a natural exponential family member but with a normally distributed block effect . The reviewed pseudo-Bayesian approach is compared to an approach based on substituting the marginal likelihood with the joint likelihood and an approach based on projections of the score function (often called quasi-likelihood). These approaches are compared for several models with normal, Poisson, and binomial conditional response distributions via the true determinant of the expected Fisher information matrix where the dispersion of the random blocks is considered a nuisance parameter. A case study using the developed methods is performed.
The joint and quasi-likelihood methods are then extended to address the case when the magnitude of random block dispersion is of concern. Again, a simulation study over several models is performed, followed by a case study when the conditional response distribution is a Poisson distribution.
The pseudo-Bayesian approach can be applied to the problem of optimal design construction under dependent observations. Often, correlation between observations exists due to restrictions on randomization. Several techniques for optimal design construction are proposed in the case of the conditional response distribution being a natural exponential family member but with a normally distributed block effect . The reviewed pseudo-Bayesian approach is compared to an approach based on substituting the marginal likelihood with the joint likelihood and an approach based on projections of the score function (often called quasi-likelihood). These approaches are compared for several models with normal, Poisson, and binomial conditional response distributions via the true determinant of the expected Fisher information matrix where the dispersion of the random blocks is considered a nuisance parameter. A case study using the developed methods is performed.
The joint and quasi-likelihood methods are then extended to address the case when the magnitude of random block dispersion is of concern. Again, a simulation study over several models is performed, followed by a case study when the conditional response distribution is a Poisson distribution.
ContributorsHassler, Edgar (Author) / Montgomery, Douglas C. (Thesis advisor) / Silvestrini, Rachel T. (Thesis advisor) / Borror, Connie M. (Committee member) / Pan, Rong (Committee member) / Arizona State University (Publisher)
Created2015
Description
Mixture experiments are useful when the interest is in determining how changes in the proportion of an experimental component affects the response. This research focuses on the modeling and design of mixture experiments when the response is categorical namely, binary and ordinal. Data from mixture experiments is characterized by the perfect collinearity of the experimental components, resulting in model matrices that are singular and inestimable under likelihood estimation procedures. To alleviate problems with estimation, this research proposes the reparameterization of two nonlinear models for ordinal data -- the proportional-odds model with a logistic link and the stereotype model. A study involving subjective ordinal responses from a mixture experiment demonstrates that the stereotype model reveals useful information about the relationship between mixture components and the ordinality of the response, which the proportional-odds fails to detect.
The second half of this research deals with the construction of exact D-optimal designs for binary and ordinal responses. For both types, the base models fall under the class of Generalized Linear Models (GLMs) with a logistic link. First, the properties of the exact D-optimal mixture designs for binary responses are investigated. It will be shown that standard mixture designs and designs proposed for normal-theory responses are poor surrogates for the true D-optimal designs. In contrast with the D-optimal designs for normal-theory responses which locate support points at the boundaries of the mixture region, exact D-optimal designs for GLMs tend to locate support points at regions of uncertainties. Alternate D-optimal designs for binary responses with high D-efficiencies are proposed by utilizing information about these regions.
The Mixture Exchange Algorithm (MEA), a search heuristic tailored to the construction of efficient mixture designs with GLM-type responses, is proposed. MEA introduces a new and efficient updating formula that lessens the computational expense of calculating the D-criterion for multi-categorical response systems, such as ordinal response models. MEA computationally outperforms comparable search heuristics by several orders of magnitude. Further, its computational expense increases at a slower rate of growth with increasing problem size. Finally, local and robust D-optimal designs for ordinal-response mixture systems are constructed using MEA, investigated, and shown to have high D-efficiency performance.
The second half of this research deals with the construction of exact D-optimal designs for binary and ordinal responses. For both types, the base models fall under the class of Generalized Linear Models (GLMs) with a logistic link. First, the properties of the exact D-optimal mixture designs for binary responses are investigated. It will be shown that standard mixture designs and designs proposed for normal-theory responses are poor surrogates for the true D-optimal designs. In contrast with the D-optimal designs for normal-theory responses which locate support points at the boundaries of the mixture region, exact D-optimal designs for GLMs tend to locate support points at regions of uncertainties. Alternate D-optimal designs for binary responses with high D-efficiencies are proposed by utilizing information about these regions.
The Mixture Exchange Algorithm (MEA), a search heuristic tailored to the construction of efficient mixture designs with GLM-type responses, is proposed. MEA introduces a new and efficient updating formula that lessens the computational expense of calculating the D-criterion for multi-categorical response systems, such as ordinal response models. MEA computationally outperforms comparable search heuristics by several orders of magnitude. Further, its computational expense increases at a slower rate of growth with increasing problem size. Finally, local and robust D-optimal designs for ordinal-response mixture systems are constructed using MEA, investigated, and shown to have high D-efficiency performance.
ContributorsMancenido, Michelle V (Author) / Montgomery, Douglas C. (Thesis advisor) / Pan, Rong (Thesis advisor) / Borror, Connie M. (Committee member) / Shunk, Dan L. (Committee member) / Arizona State University (Publisher)
Created2016
Description
The majority of research in experimental design has, to date, been focused on designs when there is only one type of response variable under consideration. In a decision-making process, however, relying on only one objective or criterion can lead to oversimplified, sub-optimal decisions that ignore important considerations. Incorporating multiple, and likely competing, objectives is critical during the decision-making process in order to balance the tradeoffs of all potential solutions. Consequently, the problem of constructing a design for an experiment when multiple types of responses are of interest does not have a clear answer, particularly when the response variables have different distributions. Responses with different distributions have different requirements of the design.
Computer-generated optimal designs are popular design choices for less standard scenarios where classical designs are not ideal. This work presents a new approach to experimental designs for dual-response systems. The normal, binomial, and Poisson distributions are considered for the potential responses. Using the D-criterion for the linear model and the Bayesian D-criterion for the nonlinear models, a weighted criterion is implemented in a coordinate-exchange algorithm. The designs are evaluated and compared across different weights. The sensitivity of the designs to the priors supplied in the Bayesian D-criterion is explored in the third chapter of this work.
The final section of this work presents a method for a decision-making process involving multiple objectives. There are situations where a decision-maker is interested in several optimal solutions, not just one. These types of decision processes fall into one of two scenarios: 1) wanting to identify the best N solutions to accomplish a goal or specific task, or 2) evaluating a decision based on several primary quantitative objectives along with secondary qualitative priorities. Design of experiment selection often involves the second scenario where the goal is to identify several contending solutions using the primary quantitative objectives, and then use the secondary qualitative objectives to guide the final decision. Layered Pareto Fronts can help identify a richer class of contenders to examine more closely. The method is illustrated with a supersaturated screening design example.
Computer-generated optimal designs are popular design choices for less standard scenarios where classical designs are not ideal. This work presents a new approach to experimental designs for dual-response systems. The normal, binomial, and Poisson distributions are considered for the potential responses. Using the D-criterion for the linear model and the Bayesian D-criterion for the nonlinear models, a weighted criterion is implemented in a coordinate-exchange algorithm. The designs are evaluated and compared across different weights. The sensitivity of the designs to the priors supplied in the Bayesian D-criterion is explored in the third chapter of this work.
The final section of this work presents a method for a decision-making process involving multiple objectives. There are situations where a decision-maker is interested in several optimal solutions, not just one. These types of decision processes fall into one of two scenarios: 1) wanting to identify the best N solutions to accomplish a goal or specific task, or 2) evaluating a decision based on several primary quantitative objectives along with secondary qualitative priorities. Design of experiment selection often involves the second scenario where the goal is to identify several contending solutions using the primary quantitative objectives, and then use the secondary qualitative objectives to guide the final decision. Layered Pareto Fronts can help identify a richer class of contenders to examine more closely. The method is illustrated with a supersaturated screening design example.
ContributorsBurke, Sarah Ellen (Author) / Montgomery, Douglas C. (Thesis advisor) / Borror, Connie M. (Thesis advisor) / Anderson-Cook, Christine M. (Committee member) / Pan, Rong (Committee member) / Silvestrini, Rachel (Committee member) / Arizona State University (Publisher)
Created2016
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
This article proposes a new information-based subdata selection (IBOSS) algorithm, Squared Scaled Distance Algorithm (SSDA). It is based on the invariance of the determinant of the information matrix under orthogonal transformations, especially rotations. Extensive simulation results show that the new IBOSS algorithm retains nice asymptotic properties of IBOSS and gives a larger determinant of the subdata information matrix. It has the same order of time complexity as the D-optimal IBOSS algorithm. However, it exploits the advantages of vectorized calculation avoiding for loops and is approximately 6 times as fast as the D-optimal IBOSS algorithm in R. The robustness of SSDA is studied from three aspects: nonorthogonality, including interaction terms and variable misspecification. A new accurate variable selection algorithm is proposed to help the implementation of IBOSS algorithms when a large number of variables are present with sparse important variables among them. Aggregating random subsample results, this variable selection algorithm is much more accurate than the LASSO method using full data. Since the time complexity is associated with the number of variables only, it is also very computationally efficient if the number of variables is fixed as n increases and not massively large. More importantly, using subsamples it solves the problem that full data cannot be stored in the memory when a data set is too large.
ContributorsZheng, Yi (Author) / Stufken, John (Thesis advisor) / Reiser, Mark R. (Committee member) / McCulloch, Robert (Committee member) / Arizona State University (Publisher)
Created2017