Matching Items (14)
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- All Subjects: Statistics
- All Subjects: Bayesian
- Creators: McCulloch, Robert
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
Cryptocurrencies have become one of the most fascinating forms of currency and economics due to their fluctuating values and lack of centralization. This project attempts to use machine learning methods to effectively model in-sample data for Bitcoin and Ethereum using rule induction methods. The dataset is cleaned by removing entries with missing data. The new column is created to measure price difference to create a more accurate analysis on the change in price. Eight relevant variables are selected using cross validation: the total number of bitcoins, the total size of the blockchains, the hash rate, mining difficulty, revenue from mining, transaction fees, the cost of transactions and the estimated transaction volume. The in-sample data is modeled using a simple tree fit, first with one variable and then with eight. Using all eight variables, the in-sample model and data have a correlation of 0.6822657. The in-sample model is improved by first applying bootstrap aggregation (also known as bagging) to fit 400 decision trees to the in-sample data using one variable. Then the random forests technique is applied to the data using all eight variables. This results in a correlation between the model and data of 9.9443413. The random forests technique is then applied to an Ethereum dataset, resulting in a correlation of 9.6904798. Finally, an out-of-sample model is created for Bitcoin and Ethereum using random forests, with a benchmark correlation of 0.03 for financial data. The correlation between the training model and the testing data for Bitcoin was 0.06957639, while for Ethereum the correlation was -0.171125. In conclusion, it is confirmed that cryptocurrencies can have accurate in-sample models by applying the random forests method to a dataset. However, out-of-sample modeling is more difficult, but in some cases better than typical forms of financial data. It should also be noted that cryptocurrency data has similar properties to other related financial datasets, realizing future potential for system modeling for cryptocurrency within the financial world.
ContributorsBrowning, Jacob Christian (Author) / Meuth, Ryan (Thesis director) / Jones, Donald (Committee member) / McCulloch, Robert (Committee member) / Computer Science and Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Several studies on cheerleading as a sport can be found in the literature; however, there is no research done on the value added to the experience at a university, to an athletic department or at a particular sport. It has been the feeling that collegiate and professional cheerleaders are not given the appropriate recognition nor credit for the amount of work they do. This contribution is sometimes in question as it depends on the school and the sports teams. The benefits are believed to vary based on the university or professional teams. This research investigated how collegiate cheerleaders and dancers add value to the university sport experience. We interviewed key personnel at the university and conference level and polled spectators at sporting events such as basketball and football. We found that the university administration and athletic personnel see the ASU Spirit Squad as value added but spectators had a totally different perspective. The university acknowledges the added value of the Spirit Squad and its necessity. Spectators attend ASU sporting events to support the university and for the entertainment. They enjoy watching the ASU Spirit Squad perform but would continue to attend ASU sporting events even if cheerleaders and dancers were not there.
ContributorsThomas, Jessica Ann (Author) / Wilson, Jeffrey (Thesis director) / Garner, Deana (Committee member) / Department of Supply Chain Management (Contributor) / Department of Marketing (Contributor) / School of Community Resources and Development (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
Problems related to alcohol consumption cause not only extra economic expenses, but are an expense to the health of both drinkers and non-drinkers due to the harm directly and indirectly caused by alcohol consumption. Investigating predictors and reasons for alcohol-related problems is of importance, as alcohol-related problems could be prevented by quitting or limiting consumption of alcohol. We were interested in predicting alcohol-related problems using multiple linear regression and regression trees, and then comparing the regressions to the tree. Impaired control, anxiety sensitivity, mother permissiveness, father permissiveness, gender, and age were included as predictors. The data used was comprised of participants (n=835) sampled from students at Arizona State University. A multiple linear regression without interactions, multiple linear regression with two-way interactions and squares, and a regression tree were used and compared. The regression and the tree had similar results. Multiple interactions of variables predicted alcohol-related problems. Overall, the tree was easier to interpret than the regressions, however, the regressions provided specific predicted alcohol-related problems scores, whereas the tree formed large groups and had a predicted alcohol-related problems score for each group. Nevertheless, the tree still predicted alcohol-related problems nearly as well, if not better than the regressions.
ContributorsVoorhies, Kirsten Reed (Author) / McCulloch, Robert (Thesis director) / Zheng, Yi (Committee member) / Patock-Peckham, Julie (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Department of Psychology (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
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
Description
This dissertation covers several topics in machine learning and causal inference. First, the question of “feature selection,” a common byproduct of regularized machine learning methods, is investigated theoretically in the context of treatment effect estimation. This involves a detailed review and extension of frameworks for estimating causal effects and in-depth theoretical study. Next, various computational approaches to estimating causal effects with machine learning methods are compared with these theoretical desiderata in mind. Several improvements to current methods for causal machine learning are identified and compelling angles for further study are pinpointed. Finally, a common method used for “explaining” predictions of machine learning algorithms, SHAP, is evaluated critically through a statistical lens.
ContributorsHerren, Andrew (Author) / Hahn, P Richard (Thesis advisor) / Kao, Ming-Hung (Committee member) / Lopes, Hedibert (Committee member) / McCulloch, Robert (Committee member) / Zhou, Shuang (Committee member) / Arizona State University (Publisher)
Created2023
Description
This dissertation develops versatile modeling tools to estimate causal effects when conditional unconfoundedness is not immediately satisfied. Chapter 2 provides a brief overview ofcommon techniques in causal inference, with a focus on models relevant to the data explored
in later chapters. The rest of the dissertation focuses on the development of novel “reduced
form” models which are designed to assess the particular challenges of different datasets.
Chapter 3 explores the question of whether or not forecasts of bankruptcy cause bankruptcy.
The question arises from the observation that companies issued going concern opinions were
more likely to go bankrupt in the following year, leading people to speculate that the opinions themselves caused the bankruptcy via a “self-fulfilling prophecy”. A Bayesian machine
learning sensitivity analysis is developed to answer this question. In exchange for additional
flexibility and fewer assumptions, this approach loses point identification of causal effects
and thus a sensitivity analysis is developed to study a wide range of plausible scenarios of
the causal effect of going concern opinions on bankruptcy. Reported in the simulations are
different performance metrics of the model in comparison with other popular methods and a
robust analysis of the sensitivity of the model to mis-specification. Results on empirical data
indicate that forecasts of bankruptcies likely do have a small causal effect.
Chapter 4 studies the effects of vaccination on COVID-19 mortality at the state level in
the United States. The dynamic nature of the pandemic complicates more straightforward
regression adjustments and invalidates many alternative models. The chapter comments on
the limitations of mechanistic approaches as well as traditional statistical methods to epidemiological data. Instead, a state space model is developed that allows the study of the
ever-changing dynamics of the pandemic’s progression. In the first stage, the model decomposes the observed mortality data into component surges, and later uses this information in
a semi-parametric regression model for causal analysis. Results are investigated thoroughly
for empirical justification and stress-tested in simulated settings.
ContributorsPapakostas, Demetrios (Author) / Hahn, Paul (Thesis advisor) / McCulloch, Robert (Committee member) / Zhou, Shuang (Committee member) / Kao, Ming-Hung (Committee member) / Lan, Shiwei (Committee member) / Arizona State University (Publisher)
Created2023