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- Creators: McCulloch, Robert
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Description
Nonregular screening designs can be an economical alternative to traditional resolution IV 2^(k-p) fractional factorials. Recently 16-run nonregular designs, referred to as no-confounding designs, were introduced in the literature. These designs have the property that no pair of main effect (ME) and two-factor interaction (2FI) estimates are completely confounded. In this dissertation, orthogonal arrays were evaluated with many popular design-ranking criteria in order to identify optimal 20-run and 24-run no-confounding designs. Monte Carlo simulation was used to empirically assess the model fitting effectiveness of the recommended no-confounding designs. The results of the simulation demonstrated that these new designs, particularly the 24-run designs, are successful at detecting active effects over 95% of the time given sufficient model effect sparsity. The final chapter presents a screening design selection methodology, based on decision trees, to aid in the selection of a screening design from a list of published options. The methodology determines which of a candidate set of screening designs has the lowest expected experimental cost.
ContributorsStone, Brian (Author) / Montgomery, Douglas C. (Thesis advisor) / Silvestrini, Rachel T. (Committee member) / Fowler, John W (Committee member) / Borror, Connie M. (Committee member) / Arizona State University (Publisher)
Created2013
Description
This dissertation explores different methodologies for combining two popular design paradigms in the field of computer experiments. Space-filling designs are commonly used in order to ensure that there is good coverage of the design space, but they may not result in good properties when it comes to model fitting. Optimal designs traditionally perform very well in terms of model fitting, particularly when a polynomial is intended, but can result in problematic replication in the case of insignificant factors. By bringing these two design types together, positive properties of each can be retained while mitigating potential weaknesses. Hybrid space-filling designs, generated as Latin hypercubes augmented with I-optimal points, are compared to designs of each contributing component. A second design type called a bridge design is also evaluated, which further integrates the disparate design types. Bridge designs are the result of a Latin hypercube undergoing coordinate exchange to reach constrained D-optimality, ensuring that there is zero replication of factors in any one-dimensional projection. Lastly, bridge designs were augmented with I-optimal points with two goals in mind. Augmentation with candidate points generated assuming the same underlying analysis model serves to reduce the prediction variance without greatly compromising the space-filling property of the design, while augmentation with candidate points generated assuming a different underlying analysis model can greatly reduce the impact of model misspecification during the design phase. Each of these composite designs are compared to pure space-filling and optimal designs. They typically out-perform pure space-filling designs in terms of prediction variance and alphabetic efficiency, while maintaining comparability with pure optimal designs at small sample size. This justifies them as excellent candidates for initial experimentation.
ContributorsKennedy, Kathryn (Author) / Montgomery, Douglas C. (Thesis advisor) / Johnson, Rachel T. (Thesis advisor) / Fowler, John W (Committee member) / Borror, Connie M. (Committee member) / Arizona State University (Publisher)
Created2013
Description
This dissertation presents methods for addressing research problems that currently can only adequately be solved using Quality Reliability Engineering (QRE) approaches especially accelerated life testing (ALT) of electronic printed wiring boards with applications to avionics circuit boards. The methods presented in this research are generally applicable to circuit boards, but the data generated and their analysis is for high performance avionics. Avionics equipment typically requires 20 years expected life by aircraft equipment manufacturers and therefore ALT is the only practical way of performing life test estimates. Both thermal and vibration ALT induced failure are performed and analyzed to resolve industry questions relating to the introduction of lead-free solder product and processes into high reliability avionics. In chapter 2, thermal ALT using an industry standard failure machine implementing Interconnect Stress Test (IST) that simulates circuit board life data is compared to real production failure data by likelihood ratio tests to arrive at a mechanical theory. This mechanical theory results in a statistically equivalent energy bound such that failure distributions below a specific energy level are considered to be from the same distribution thus allowing testers to quantify parameter setting in IST prior to life testing. In chapter 3, vibration ALT comparing tin-lead and lead-free circuit board solder designs involves the use of the likelihood ratio (LR) test to assess both complete failure data and S-N curves to present methods for analyzing data. Failure data is analyzed using Regression and two-way analysis of variance (ANOVA) and reconciled with the LR test results that indicating that a costly aging pre-process may be eliminated in certain cases. In chapter 4, vibration ALT for side-by-side tin-lead and lead-free solder black box designs are life tested. Commercial models from strain data do not exist at the low levels associated with life testing and need to be developed because testing performed and presented here indicate that both tin-lead and lead-free solders are similar. In addition, earlier failures due to vibration like connector failure modes will occur before solder interconnect failures.
ContributorsJuarez, Joseph Moses (Author) / Montgomery, Douglas C. (Thesis advisor) / Borror, Connie M. (Thesis advisor) / Gel, Esma (Committee member) / Mignolet, Marc (Committee member) / Pan, Rong (Committee member) / Arizona State University (Publisher)
Created2012
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
The primary objective in time series analysis is forecasting. Raw data often exhibits nonstationary behavior: trends, seasonal cycles, and heteroskedasticity. After data is transformed to a weakly stationary process, autoregressive moving average (ARMA) models may capture the remaining temporal dynamics to improve forecasting. Estimation of ARMA can be performed through regressing current values on previous realizations and proxy innovations. The classic paradigm fails when dynamics are nonlinear; in this case, parametric, regime-switching specifications model changes in level, ARMA dynamics, and volatility, using a finite number of latent states. If the states can be identified using past endogenous or exogenous information, a threshold autoregressive (TAR) or logistic smooth transition autoregressive (LSTAR) model may simplify complex nonlinear associations to conditional weakly stationary processes. For ARMA, TAR, and STAR, order parameters quantify the extent past information is associated with the future. Unfortunately, even if model orders are known a priori, the possibility of over-fitting can lead to sub-optimal forecasting performance. By intentionally overestimating these orders, a linear representation of the full model is exploited and Bayesian regularization can be used to achieve sparsity. Global-local shrinkage priors for AR, MA, and exogenous coefficients are adopted to pull posterior means toward 0 without over-shrinking relevant effects. This dissertation introduces, evaluates, and compares Bayesian techniques that automatically perform model selection and coefficient estimation of ARMA, TAR, and STAR models. Multiple Monte Carlo experiments illustrate the accuracy of these methods in finding the "true" data generating process. Practical applications demonstrate their efficacy in forecasting.
ContributorsGiacomazzo, Mario (Author) / Kamarianakis, Yiannis (Thesis advisor) / Reiser, Mark R. (Committee member) / McCulloch, Robert (Committee member) / Hahn, Richard (Committee member) / Fricks, John (Committee member) / Arizona State University (Publisher)
Created2018
Description
This dissertation investigates the classification of systemic lupus erythematosus (SLE) in the presence of non-SLE alternatives, while developing novel curve classification methodologies with wide ranging applications. Functional data representations of plasma thermogram measurements and the corresponding derivative curves provide predictors yet to be investigated for SLE identification. Functional nonparametric classifiers form a methodological basis, which is used herein to develop a) the family of ESFuNC segment-wise curve classification algorithms and b) per-pixel ensembles based on logistic regression and fused-LASSO. The proposed methods achieve test set accuracy rates as high as 94.3%, while returning information about regions of the temperature domain that are critical for population discrimination. The undertaken analyses suggest that derivate-based information contributes significantly in improved classification performance relative to recently published studies on SLE plasma thermograms.
ContributorsBuscaglia, Robert, Ph.D (Author) / Kamarianakis, Yiannis (Thesis advisor) / Armbruster, Dieter (Committee member) / Lanchier, Nicholas (Committee member) / McCulloch, Robert (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2018
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
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
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