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This thesis proposes novel methods to address specific challenges in analyzing the frequency- and time-domain properties of nonstationary time series data motivated by the study of electrophysiological signals. A new method is proposed for the simultaneous and automatic analysis of the association between the time-varying power spectrum and covariates. The procedure adaptively partitions the grid of time and covariate values into an unknown number of approximately stationary blocks and nonparametrically estimates local spectra within blocks through penalized splines. The approach is formulated in a fully Bayesian framework, in which the number and locations of partition points are random, and fit using reversible jump Markov chain Monte Carlo techniques. Estimation and inference averaged over the distribution of partitions allows for the accurate analysis of spectra with both smooth and abrupt changes. The new methodology is used to analyze the association between the time-varying spectrum of heart rate variability and self-reported sleep quality in a study of older adults serving as the primary caregiver for their ill spouse. Another method proposed in this dissertation develops a unique framework for automatically identifying bands of frequencies exhibiting similar nonstationary behavior. This proposal provides a standardized, unifying approach to constructing customized frequency bands for different signals under study across different settings. A frequency-domain, iterative cumulative sum procedure is formulated to identify frequency bands that exhibit similar nonstationary patterns in the power spectrum through time. A formal hypothesis testing procedure is also developed to test which, if any, frequency bands remain stationary. This method is shown to consistently estimate the number of frequency bands and the location of the upper and lower bounds defining each frequency band. This method is used to estimate frequency bands useful in summarizing nonstationary behavior of full night heart rate variability data. / Statistics

This dissertation consists of three manuscripts analyzing labor market dynamics in West Virginia and the Appalachian Region. The first manuscript examines the dynamic effects of national, regional, and local labor market shocks on labor force participation rates in Appalachia. A dynamic factor model with time-varying loading parameters and stochastic volatility is used to explore the synchronicity and divergence between state labor force participation rates within and outside the Appalachian region. We find that the choice of time and state is crucial to the relative importance of the level of synchronization on observed change in LFPR variations. Our findings can help better target labor policy by taking advantage of the sensitivity exhibited by each state to various labor market conditions. The second manuscript examines the dynamic effects of state, Metro/Non-Metro, and county labor market shocks on labor force participation rates in West Virginia. In the first stage, using a dynamic factor model, we find that non-metropolitan and county-specific components are dominant contributors to the observed variations in the change in West Virginia LFPRs. In the second stage, using a fixed effects panel model, we find county demographics, education levels, income, access to interstate highways, and industry composition are useful covariates for explaining the variance contributions of the state, metro/non-metro and county factors. The third manuscript uses cointegration analysis in the presence of structural breaks to determine whether the Unemployment Invariance Hypothesis exists in West Virginia. Using monthly labor force data from 1976 - 2022, we find mixed support for the unemployment invariance, added worker effect, and discouraged worker effect hypotheses over multiple sub-sample periods. These results suggest that labor markets are temporally-dynamic, and a one-size-fits-all approach could prove disadvantageous to growth. / Doctor of Philosophy / This dissertation focuses on labor market dynamics in West Virginia and the Appalachian Region. In the first of three manuscripts, we investigate how much U.S. state labor force participation rates move together nationally, and within the Appalachian Region. We find that how much labor force participation rates move together across the U.S. and within the Appalachian Region depends on the choice of time and state. In the second manuscript, we examine how much West Virginia county labor force participation rates move together across the state and within the Metropolitan and Non-Metropolitan regions. We also study how county characteristics such as industry composition and education levels influence the variation in how much labor force participation rates move together. We find that Non-metropolitan county labor force participation rates exhibit similar dynamic behavior and that education, personal income, access to highways, and industry composition of the counties influences how much the rates move together at the different levels. In the third manuscript, we investigate whether changes in the unemployment rate in West Virginia result influences that state's labor force participation rate in the long-run. We find that evidence of said long-run relationship albeit changing over time. We posit that the relationship dynamics are largely explained by the ensuing labor market and economic conditions. By extension, labor market policies and interventions should be timely and flexible.

Statistical process monitoring and hierarchical Bayesian modeling are two ways to learn more about processes of interest. In this work, we consider two main components: risk-adjusted monitoring and Bayesian hierarchical models for spatial data. Usually, if prior information about a process is known, it is important to incorporate this into the monitoring scheme. For example, when monitoring 30-day mortality rates after surgery, the pre-operative risk of patients based on health characteristics is often an indicator of how likely the surgery is to succeed. In these cases, risk-adjusted monitoring techniques are used. In this work, the practical limitations of the traditional implementation of risk-adjusted monitoring methods are discussed and an improved implementation is proposed. A method to perform spatial risk-adjustment based on exact locations of concurrent observations to account for spatial dependence is also described. Furthermore, the development of objective priors for fully Bayesian hierarchical models for areal data is explored for Gaussian responses. Collectively, these statistical methods serve as analytic tools to better monitor and model spatial processes. / Ph. D. / The purpose of this research was to advance understanding of help-seeking behaviors of lowincome older adults who were deemed ineligible to receive state-funded assistance. I used health services data from two independent state agencies to assess factors associated with service use and health status; follow-up interviews were conducted to explore self-management strategies of rural older adults with unmet needs. Older adults who did not receive help were at increased risk for hospitalization and mortality compared to individuals who received helped. Rural older adults were significantly more likely to not receive help and were at increased risk for mortality, placing them in a vulnerable position. Interviews with rural-dwelling older adults that were not receiving help highlighted the challenges associated with living with unmet needs but demonstrated resilience through their use of physical and psychological coping mechanisms to navigate daily challenges and maintain health and well-being. They had to deal with numerous difficulties performing instrumental activities of daily living (IADL); mobility was an underlying problem that led to subsequent IADL limitations, such as difficulty with household chores and meal preparation. Policymakers need to advocate for services that allow older adults to address preemptively their care needs before they become unmanageable. Ensuring the availability of services for near-risk older adults who are proactive in addressing their functional care needs would benefit individuals and caregivers on whom they rely. Such services not only support older adults’ health, functioning, and well-being but may be cost-effective for public programs. Policies should reduce unmet needs among older adults by increasing service access in rural communities because even if services exist, they may not be available to this near-risk population of older adults.Many current scientific applications involve data collection that has some type of spatial component. Within these applications, the objective could be to monitor incoming data in order to quickly detect any changes in real time. Another objective could be to use statistical models to characterize and understand the underlying features of the data. In this work, we develop statistical methodology to monitor and model data that include a spatial component. Specifically, we develop a monitoring scheme that adjusts for spatial risk and present an objective way to quantify and model spatial dependence when data is measured for areal units. Collectively, the statistical methods developed in this work serve as analytic tools to better monitor and model spatial data.

Central to the study of Life is knowledge both about the underlying relationships among living things and the processes that have molded them into their diverse forms. Phylogenetics provides a powerful toolkit for investigating both aspects. Bayesian phylogenetics has gained much popularity, due to its readily interpretable notion of probability. However, the posterior probability of a phylogeny, as well as any dependent biological inferences, is conditioned on the assumed model of evolution and its priors, necessitating care in model formulation. In Chapter 1, I outline the Bayesian perspective of phylogenetic inference and provide my view on its most outstanding questions. I then present results from three studies that aim to (i) improve the accuracy of Bayesian phylogenetic inference and (ii) assess when the model assumed in a Bayesian analysis is insufficient to produce an accurate phylogenetic estimate. As phylogenetic data sets increase in size, they must also accommodate a greater diversity of underlying evolutionary processes. Partitioned models represent one way of accounting for this heterogeneity. In Chapter 2, I describe a simulation study to investigate whether support for partitioning of empirical data sets represents a real signal of heterogeneity or whether it is merely a statistical artifact. The results suggest that empirical data are extremely heterogeneous. The incorporation of heterogeneity into inferential models is important for accurate phylogenetic inference. Bayesian phylogenetic estimates of branch lengths are often wildly unreasonable. However, branch lengths are important input for many other analyses. In Chapter 3, I study the occurrence of this phenomenon, identify the data sets most likely to be affected, demonstrate the causes of the bias, and suggest several solutions to avoid inaccurate inferences. Phylogeneticists rarely assess absolute fit between an assumed model of evolution and the data being analyzed. While an approach to assessing fit in a Bayesian framework has been proposed, it sometimes performs quite poorly in predicting a model’s phylogenetic utility. In Chapter 4, I propose and evaluate new test statistics for assessing phylogenetic model adequacy, which directly evaluate a model’s phylogenetic performance. / text

Harm reduction strategies can mitigate against some of the deleterious effects of alcohol on families. These strategies are most feasible and cost-effective when they can be targeted at those who are most at risk. Previous studies examining the relation between parents’ alcohol use and their children’s psychological adjustment have failed to consider important contextual questions such as drinking motives. The current investigation set out to identify the extent to which parents’ drinking motives predict internalizing and externalizing psychopathology in their children. The investigation consisted of cross sectional analysis of parents’ drinking motives and their children’s adjustment using data from 154 families recruited from the local community. Utilizing Bayesian data analytic techniques, we examined the role of parents’ drinking motives along with possible mediating variables including familial conflict, parental depression, and parenting style. Results showed that maternal social drinking motives were better predictors of children’s maladjustment than either coping or enhancement drinking motives. Unexpectedly, maternal enhancement drinking motives were associated with fewer adjustment problems. Maternal enhancement drinking motives also predicted higher levels of collaborative conflict resolution and lower levels of parental depression, both of which were associated with reduced levels of children’s externalizing problems. Paternal alcohol consumption and drinking motives were not associated with children’s internalizing or externalizing problems. Clinical implications and directions for future research are discussed.

Doctor of Philosophy / Department of Statistics / Paul Nelson / Panels of judges are often used to estimate consumer preferences for m items such as food products. Judges can either evaluate each item on several ordinal scales and indirectly produce an overall ranking, or directly report a ranking of the items. A complete ranking orders all the items from best to worst. A partial ranking, as we use the term, only reports rankings of the best q out of m items. Direct ranking, the subject of this report, does not require the widespread but questionable practice of treating ordinal measurement as though they were on ratio or interval scales. Here, we develop and study segmentation models in which the panel may consist of relatively homogeneous subgroups, the segments. Judges within a subgroup will tend to agree among themselves and differ from judges in the other subgroups. We develop and study the statistical analysis of mixture models where it is not known to which segment a judge belongs or in some cases how many segments there are. Viewing segment membership indicator variables as latent data, an E-M algorithm was used to find the maximum likelihood estimators of the parameters specifying a mixture of Mallow’s (1957) distance models for complete and partial rankings. A simulation study was conducted to evaluate the behavior of the E-M algorithm in terms of such issues as the fraction of data sets for which the algorithm fails to converge and the sensitivity of initial values to the convergence rate and the performance of the maximum likelihood estimators in terms of bias and mean square error, where applicable. A Bayesian approach was developed and credible set estimators was constructed. Simulation was used to evaluate the performance of these credible sets as confidence sets. A method for predicting segment membership from covariates measured on a judge was derived using a logistic model applied to a mixture of Mallows probability distance models. The effects of covariates on segment membership were assessed. Likelihood sets for parameters specifying mixtures of Mallows distance models were constructed and explored.

I present a comprehensive investigation of fast stars in the Milky Way, from brisk disc stars to stars escaping the Galaxy. My thesis is that fast stars are the smoking guns of extreme stellar collisions and explosions, and so can act as an intermediary to studying these theoretically-unconquered astrophysical processes. In Chapter 1 I give a history of fast stars, address what it means for a star to be fast, and describe the processes that accelerate stars. I concisely summarise the Gaia mission, whose recent data releases heavily influenced this thesis. Supernovae in binary systems can fling away the companion; if a runaway companion can be associated with a supernova remnant, then together they reveal the evolution that led to the supernova. However, these associations are difficult to establish. In Ch. 2, I develop a sophisticated Bayesian methodology to search the nearest ten remnants for a companion, by combining data from Gaia DR1 with a 3D dust-map and binary population synthesis. With Gaia DR2, I will identify companions of tens of supernova remnants and thus open a new window to studying late-stage stellar evolution. It is unknown why 17% of B stars are spinning near break-up; these stars are termed Be stars because of emission lines from their ejected material. Their rapid spin could be due to mass transfer, but in Ch. 3 I show this would create runaway Be stars. I demonstrate using a hierarchical Bayesian model that these exist in sufficient numbers, and thus that all Be stars may arise from mass transfer. The stars escaping the Milky Way are termed hypervelocity stars. In Ch. 4, I overturn the consensus that the hypervelocity stars originated in the Galactic centre by showing that a Large Magellanic Cloud (LMC) origin better explains their distribution on the sky. In Ch. 5 I present three ground-breaking hypervelocity results with Gaia DR2: 1) only 41 of the 524 hypervelocity star candidates are truly escaping, 2) at least one of the hypervelocity stars originates in the LMC, and 3) the discovery of three hypervelocity white dwarf runaways from thermonuclear supernovae.