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- All Subjects: Bayesian statistical decision theory
- Creators: Levy, Roy
- Creators: Zhang, Junshan
Description
Electrical neural activity detection and tracking have many applications in medical research and brain computer interface technologies. In this thesis, we focus on the development of advanced signal processing algorithms to track neural activity and on the mapping of these algorithms onto hardware to enable real-time tracking. At the heart of these algorithms is particle filtering (PF), a sequential Monte Carlo technique used to estimate the unknown parameters of dynamic systems. First, we analyze the bottlenecks in existing PF algorithms, and we propose a new parallel PF (PPF) algorithm based on the independent Metropolis-Hastings (IMH) algorithm. We show that the proposed PPF-IMH algorithm improves the root mean-squared error (RMSE) estimation performance, and we demonstrate that a parallel implementation of the algorithm results in significant reduction in inter-processor communication. We apply our implementation on a Xilinx Virtex-5 field programmable gate array (FPGA) platform to demonstrate that, for a one-dimensional problem, the PPF-IMH architecture with four processing elements and 1,000 particles can process input samples at 170 kHz by using less than 5% FPGA resources. We also apply the proposed PPF-IMH to waveform-agile sensing to achieve real-time tracking of dynamic targets with high RMSE tracking performance. We next integrate the PPF-IMH algorithm to track the dynamic parameters in neural sensing when the number of neural dipole sources is known. We analyze the computational complexity of a PF based method and propose the use of multiple particle filtering (MPF) to reduce the complexity. We demonstrate the improved performance of MPF using numerical simulations with both synthetic and real data. We also propose an FPGA implementation of the MPF algorithm and show that the implementation supports real-time tracking. For the more realistic scenario of automatically estimating an unknown number of time-varying neural dipole sources, we propose a new approach based on the probability hypothesis density filtering (PHDF) algorithm. The PHDF is implemented using particle filtering (PF-PHDF), and it is applied in a closed-loop to first estimate the number of dipole sources and then their corresponding amplitude, location and orientation parameters. We demonstrate the improved tracking performance of the proposed PF-PHDF algorithm and map it onto a Xilinx Virtex-5 FPGA platform to show its real-time implementation potential. Finally, we propose the use of sensor scheduling and compressive sensing techniques to reduce the number of active sensors, and thus overall power consumption, of electroencephalography (EEG) systems. We propose an efficient sensor scheduling algorithm which adaptively configures EEG sensors at each measurement time interval to reduce the number of sensors needed for accurate tracking. We combine the sensor scheduling method with PF-PHDF and implement the system on an FPGA platform to achieve real-time tracking. We also investigate the sparsity of EEG signals and integrate compressive sensing with PF to estimate neural activity. Simulation results show that both sensor scheduling and compressive sensing based methods achieve comparable tracking performance with significantly reduced number of sensors.
ContributorsMiao, Lifeng (Author) / Chakrabarti, Chaitali (Thesis advisor) / Papandreou-Suppappola, Antonia (Thesis advisor) / Zhang, Junshan (Committee member) / Bliss, Daniel (Committee member) / Kovvali, Narayan (Committee member) / Arizona State University (Publisher)
Created2013
Description
This simulation study compared the utility of various discrepancy measures within a posterior predictive model checking (PPMC) framework for detecting different types of data-model misfit in multidimensional Bayesian network (BN) models. The investigated conditions were motivated by an applied research program utilizing an operational complex performance assessment within a digital-simulation educational context grounded in theories of cognition and learning. BN models were manipulated along two factors: latent variable dependency structure and number of latent classes. Distributions of posterior predicted p-values (PPP-values) served as the primary outcome measure and were summarized in graphical presentations, by median values across replications, and by proportions of replications in which the PPP-values were extreme. An effect size measure for PPMC was introduced as a supplemental numerical summary to the PPP-value. Consistent with previous PPMC research, all investigated fit functions tended to perform conservatively, but Standardized Generalized Dimensionality Discrepancy Measure (SGDDM), Yen's Q3, and Hierarchy Consistency Index (HCI) only mildly so. Adequate power to detect at least some types of misfit was demonstrated by SGDDM, Q3, HCI, Item Consistency Index (ICI), and to a lesser extent Deviance, while proportion correct (PC), a chi-square-type item-fit measure, Ranked Probability Score (RPS), and Good's Logarithmic Scale (GLS) were powerless across all investigated factors. Bivariate SGDDM and Q3 were found to provide powerful and detailed feedback for all investigated types of misfit.
ContributorsCrawford, Aaron (Author) / Levy, Roy (Thesis advisor) / Green, Samuel (Committee member) / Thompson, Marilyn (Committee member) / Arizona State University (Publisher)
Created2014
Description
Research methods based on the frequentist philosophy use prior information in a priori power calculations and when determining the necessary sample size for the detection of an effect, but not in statistical analyses. Bayesian methods incorporate prior knowledge into the statistical analysis in the form of a prior distribution. When prior information about a relationship is available, the estimates obtained could differ drastically depending on the choice of Bayesian or frequentist method. Study 1 in this project compared the performance of five methods for obtaining interval estimates of the mediated effect in terms of coverage, Type I error rate, empirical power, interval imbalance, and interval width at N = 20, 40, 60, 100 and 500. In Study 1, Bayesian methods with informative prior distributions performed almost identically to Bayesian methods with diffuse prior distributions, and had more power than normal theory confidence limits, lower Type I error rates than the percentile bootstrap, and coverage, interval width, and imbalance comparable to normal theory, percentile bootstrap, and the bias-corrected bootstrap confidence limits. Study 2 evaluated if a Bayesian method with true parameter values as prior information outperforms the other methods. The findings indicate that with true values of parameters as the prior information, Bayesian credibility intervals with informative prior distributions have more power, less imbalance, and narrower intervals than Bayesian credibility intervals with diffuse prior distributions, normal theory, percentile bootstrap, and bias-corrected bootstrap confidence limits. Study 3 examined how much power increases when increasing the precision of the prior distribution by a factor of ten for either the action or the conceptual path in mediation analysis. Power generally increases with increases in precision but there are many sample size and parameter value combinations where precision increases by a factor of 10 do not lead to substantial increases in power.
ContributorsMiocevic, Milica (Author) / Mackinnon, David P. (Thesis advisor) / Levy, Roy (Committee member) / West, Stephen G. (Committee member) / Enders, Craig (Committee member) / Arizona State University (Publisher)
Created2014
Description
Many methodological approaches have been utilized to predict student retention and persistence over the years, yet few have utilized a Bayesian framework. It is believed this is due in part to the absence of an established process for guiding educational researchers reared in a frequentist perspective into the realms of Bayesian analysis and educational data mining. The current study aimed to address this by providing a model-building process for developing a Bayesian network (BN) that leveraged educational data mining, Bayesian analysis, and traditional iterative model-building techniques in order to predict whether community college students will stop out at the completion of each of their first six terms. The study utilized exploratory and confirmatory techniques to reduce an initial pool of more than 50 potential predictor variables to a parsimonious final BN with only four predictor variables. The average in-sample classification accuracy rate for the model was 80% (Cohen's κ = 53%). The model was shown to be generalizable across samples with an average out-of-sample classification accuracy rate of 78% (Cohen's κ = 49%). The classification rates for the BN were also found to be superior to the classification rates produced by an analog frequentist discrete-time survival analysis model.
ContributorsArcuria, Philip (Author) / Levy, Roy (Thesis advisor) / Green, Samuel B (Committee member) / Thompson, Marilyn S (Committee member) / Arizona State University (Publisher)
Created2015
Description
This thesis examines the application of statistical signal processing approaches to data arising from surveys intended to measure psychological and sociological phenomena underpinning human social dynamics. The use of signal processing methods for analysis of signals arising from measurement of social, biological, and other non-traditional phenomena has been an important and growing area of signal processing research over the past decade. Here, we explore the application of statistical modeling and signal processing concepts to data obtained from the Global Group Relations Project, specifically to understand and quantify the effects and interactions of social psychological factors related to intergroup conflicts. We use Bayesian networks to specify prospective models of conditional dependence. Bayesian networks are determined between social psychological factors and conflict variables, and modeled by directed acyclic graphs, while the significant interactions are modeled as conditional probabilities. Since the data are sparse and multi-dimensional, we regress Gaussian mixture models (GMMs) against the data to estimate the conditional probabilities of interest. The parameters of GMMs are estimated using the expectation-maximization (EM) algorithm. However, the EM algorithm may suffer from over-fitting problem due to the high dimensionality and limited observations entailed in this data set. Therefore, the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) are used for GMM order estimation. To assist intuitive understanding of the interactions of social variables and the intergroup conflicts, we introduce a color-based visualization scheme. In this scheme, the intensities of colors are proportional to the conditional probabilities observed.
ContributorsLiu, Hui (Author) / Taylor, Thomas (Thesis advisor) / Cochran, Douglas (Thesis advisor) / Zhang, Junshan (Committee member) / Arizona State University (Publisher)
Created2012
Description
Dynamic Bayesian networks (DBNs; Reye, 2004) are a promising tool for modeling student proficiency under rich measurement scenarios (Reichenberg, in press). These scenarios often present assessment conditions far more complex than what is seen with more traditional assessments and require assessment arguments and psychometric models capable of integrating those complexities. Unfortunately, DBNs remain understudied and their psychometric properties relatively unknown. If the apparent strengths of DBNs are to be leveraged, then the body of literature surrounding their properties and use needs to be expanded upon. To this end, the current work aimed at exploring the properties of DBNs under a variety of realistic psychometric conditions. A two-phase Monte Carlo simulation study was conducted in order to evaluate parameter recovery for DBNs using maximum likelihood estimation with the Netica software package. Phase 1 included a limited number of conditions and was exploratory in nature while Phase 2 included a larger and more targeted complement of conditions. Manipulated factors included sample size, measurement quality, test length, the number of measurement occasions. Results suggested that measurement quality has the most prominent impact on estimation quality with more distinct performance categories yielding better estimation. While increasing sample size tended to improve estimation, there were a limited number of conditions under which greater samples size led to more estimation bias. An exploration of this phenomenon is included. From a practical perspective, parameter recovery appeared to be sufficient with samples as low as N = 400 as long as measurement quality was not poor and at least three items were present at each measurement occasion. Tests consisting of only a single item required exceptional measurement quality in order to adequately recover model parameters. The study was somewhat limited due to potentially software-specific issues as well as a non-comprehensive collection of experimental conditions. Further research should replicate and, potentially expand the current work using other software packages including exploring alternate estimation methods (e.g., Markov chain Monte Carlo).
ContributorsReichenberg, Raymond E (Author) / Levy, Roy (Thesis advisor) / Eggum-Wilkens, Natalie (Thesis advisor) / Iida, Masumi (Committee member) / DeLay, Dawn (Committee member) / Arizona State University (Publisher)
Created2018
Description
Accurate data analysis and interpretation of results may be influenced by many potential factors. The factors of interest in the current work are the chosen analysis model(s), the presence of missing data, and the type(s) of data collected. If analysis models are used which a) do not accurately capture the structure of relationships in the data such as clustered/hierarchical data, b) do not allow or control for missing values present in the data, or c) do not accurately compensate for different data types such as categorical data, then the assumptions associated with the model have not been met and the results of the analysis may be inaccurate. In the presence of clustered
ested data, hierarchical linear modeling or multilevel modeling (MLM; Raudenbush & Bryk, 2002) has the ability to predict outcomes for each level of analysis and across multiple levels (accounting for relationships between levels) providing a significant advantage over single-level analyses. When multilevel data contain missingness, multilevel multiple imputation (MLMI) techniques may be used to model both the missingness and the clustered nature of the data. With categorical multilevel data with missingness, categorical MLMI must be used. Two such routines for MLMI with continuous and categorical data were explored with missing at random (MAR) data: a formal Bayesian imputation and analysis routine in JAGS (R/JAGS) and a common MLM procedure of imputation via Bayesian estimation in BLImP with frequentist analysis of the multilevel model in Mplus (BLImP/Mplus). Manipulated variables included interclass correlations, number of clusters, and the rate of missingness. Results showed that with continuous data, R/JAGS returned more accurate parameter estimates than BLImP/Mplus for almost all parameters of interest across levels of the manipulated variables. Both R/JAGS and BLImP/Mplus encountered convergence issues and returned inaccurate parameter estimates when imputing and analyzing dichotomous data. Follow-up studies showed that JAGS and BLImP returned similar imputed datasets but the choice of analysis software for MLM impacted the recovery of accurate parameter estimates. Implications of these findings and recommendations for further research will be discussed.
ested data, hierarchical linear modeling or multilevel modeling (MLM; Raudenbush & Bryk, 2002) has the ability to predict outcomes for each level of analysis and across multiple levels (accounting for relationships between levels) providing a significant advantage over single-level analyses. When multilevel data contain missingness, multilevel multiple imputation (MLMI) techniques may be used to model both the missingness and the clustered nature of the data. With categorical multilevel data with missingness, categorical MLMI must be used. Two such routines for MLMI with continuous and categorical data were explored with missing at random (MAR) data: a formal Bayesian imputation and analysis routine in JAGS (R/JAGS) and a common MLM procedure of imputation via Bayesian estimation in BLImP with frequentist analysis of the multilevel model in Mplus (BLImP/Mplus). Manipulated variables included interclass correlations, number of clusters, and the rate of missingness. Results showed that with continuous data, R/JAGS returned more accurate parameter estimates than BLImP/Mplus for almost all parameters of interest across levels of the manipulated variables. Both R/JAGS and BLImP/Mplus encountered convergence issues and returned inaccurate parameter estimates when imputing and analyzing dichotomous data. Follow-up studies showed that JAGS and BLImP returned similar imputed datasets but the choice of analysis software for MLM impacted the recovery of accurate parameter estimates. Implications of these findings and recommendations for further research will be discussed.
ContributorsKunze, Katie L (Author) / Levy, Roy (Thesis advisor) / Enders, Craig K. (Committee member) / Thompson, Marilyn S (Committee member) / Arizona State University (Publisher)
Created2016
Description
Statistical mediation analysis has been widely used in the social sciences in order to examine the indirect effects of an independent variable on a dependent variable. The statistical properties of the single mediator model with manifest and latent variables have been studied using simulation studies. However, the single mediator model with latent variables in the Bayesian framework with various accurate and inaccurate priors for structural and measurement model parameters has yet to be evaluated in a statistical simulation. This dissertation outlines the steps in the estimation of a single mediator model with latent variables as a Bayesian structural equation model (SEM). A Monte Carlo study is carried out in order to examine the statistical properties of point and interval summaries for the mediated effect in the Bayesian latent variable single mediator model with prior distributions with varying degrees of accuracy and informativeness. Bayesian methods with diffuse priors have equally good statistical properties as Maximum Likelihood (ML) and the distribution of the product. With accurate informative priors Bayesian methods can increase power up to 25% and decrease interval width up to 24%. With inaccurate informative priors the point summaries of the mediated effect are more biased than ML estimates, and the bias is higher if the inaccuracy occurs in priors for structural parameters than in priors for measurement model parameters. Findings from the Monte Carlo study are generalizable to Bayesian analyses with priors of the same distributional forms that have comparable amounts of (in)accuracy and informativeness to priors evaluated in the Monte Carlo study.
ContributorsMiočević, Milica (Author) / Mackinnon, David P. (Thesis advisor) / Levy, Roy (Thesis advisor) / Grimm, Kevin (Committee member) / West, Stephen G. (Committee member) / Arizona State University (Publisher)
Created2017