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The dynamic structural equation modeling (DSEM) framework incorporates hierarchical latent modeling (HLM), structural equation modeling (SEM), time series analysis (TSA), and time-varying effects modeling (TVEM) to model the dynamic relationship between latent and observed variables. To model the functional relationships between variables, a Gaussian process (GP), by definition of its covariance function(s), allows researchers to define Gaussian distributions over functions of input variables. Therefore, by incorporating GPs to model the presence of significant trend in either latent or observed variables, this dissertation explores the adequacy and performance of GPs in manipulated conditions of sample size using the flexible Bayesian analysis approach. The overall results of these Monte Carlo simulation studies showcase the ability of the multi-output GPs to properly explore the presence of trends. Also, in modeling intensive longitudinal data, GPs can be specified to properly account for trends, without generating significantly biased and imprecise estimates.

Converting exotic forages to native warm-season grasses (NWSG) such as big bluestem (Andropogon gerardii), little bluestem (Schizachyrium scoparium), and Indian grass (Sorghastrum nutans) offers a sustainable alternative because NWSG may yield comparative livestock gains with less fertilizer, as well as offer habitat for arthropods and declining grassland bird species such as Dickcissels (Spiza americana). In the Southeastern United States, the predominant forage species are exotics such as bermudagrass (Cynodon dactylon) and tall fescue (Schedonorus arundinaceus), so NWSG conversion could substantially improve sustainability and wildlife habitat on private lands in the region. In 2011 and 2012, I studied response of Dickcissels and arthropods to forage origin, diversity, and grazing at the Mississippi State University Prairie Research Unit in Monroe Co., MS, USA. Four treatments were established among 12 pastures representing a gradient in management intensity, including a grazed bermudagrass and tall fescue mix (GMEP), grazed Indian grass monoculture (GINP), grazed mixed native pasture (GMNP), and a non-grazed mixed native pasture (NMNP). Grazed treatments were stocked with steers from May through August each year. I also evaluated the economic implications of each grazing system. In general, there was a positive response to native grasses among Dickcissels and arthropods and a negative effect from grazing. Dickcissel productivity (fledgling/ha) was highest in NMNP and lowest in GMEP, whereas productivity was intermediate and similar among grazed native pastures. This pattern was attributable to availability of suitable nest sites because nest survival and brood size did not vary by treatment. Several arthropod taxa responded positively to greater vegetation density in NMNP, but communities were largely similar among grazed pastures irrespective of forage origin or diversity, suggesting little short-term response to NWSG. In spite of unfavorable growing conditions due to drought, cattle grazing NWSG consistently outperformed conspecifics in GMEP, with 45–72% higher average daily gain. Partial budget analysis indicated that NWSG pastures yielded up to 36% marginal rates of return despite establishment costs. These results suggest NWSG conversion can benefit tall grass specialists such as Dickcissels while offering competitive alternatives to exotic forages, resulting in net benefits for both conservationists and producers.

Growing concerns about climate change, foreign oil dependency, and environmental quality have fostered interest in perennial native grasses (e.g. switchgrass [Panicum virgatum]) for bioenergy production while also maintaining biodiversity and ecosystem function. However, biofuel cultivation in marginal landscapes such as airport grasslands may have detrimental effects on aviation safety as well as demography and conservation efforts for grassland birds including Dickcissels (Spiza americana). In 2011–2013 I studied the response of avian populations to vegetation composition and harvest frequency of switchgrass monocultures and native warm-season grass (NWSG) mixtures at B. Bryan farms in Clay Co. MS, USA. Four treatments incorporating switchgrass and NWSG with single and multiple annual harvesting were established on 16 experimental plots. I examined the relative abundance, aviation risk, and conservation value of birds associated with these treatments, evaluated contributions of habitat attributes and individual male quality towards territory productivity and determined effects of harvest regimens on nest success, nest density, and productivity for Dickcissels. Avian relative abundance was greater in switchgrass plots during winter months, whereas NWSG was favored by species during the breeding season. Conversely, treatment differences in aviation risk and conservation value were not biologically significant. Only 2.6% of observations included avian species of high risk to aircraft, suggesting that it may be feasible to use semi-natural grasslands at airports to provide grassland bird habitat while concurrently minimizing aviation risk. Regarding individual and habitat quality effects on nest survival and productivity, male song rate was not an effective surrogate for individual quality in demographic models. However, nest survival declined with increasing territory size and territories established earlier in the season had greater territory productivity relative to later arriving males, providing evidence that some metric of individual quality is important for grassland bird reproduction. Additionally, vegetation composition and harvest frequencies influenced nest density and productivity, but not nest survival. Native warm season grasses contained 54–64 times more nests relative to switchgrass treatments, and nest density was 10% greater in single harvest plots. My results suggest semi-natural grasslands can support grassland bird conservation while allowing for biofuel production and aviation risk management in airport landscapes.

<p>Clinical trials are the gold standard for inferring the causal effects of treatments or interventions. This thesis is concerned with the development of methodologies for two problems in modern clinical trials. First is analyzing binary repeated measures in clinical trials using models that reflect the complicated autocorrelation patterns in the data, so as to obtain high power when inferring treatment effects. Second is simulating realistic outcomes and subject nonadherence mechanisms in Phase III pharmaceutical clinical trials under the Tripartite Framework.</p><p> </p><p><b>Bayesian Models for Binary Repeated Data: The Bayesian General Logistic Autoregressive Model and the Polya-Gamma Logistic Autoregressive Model</b></p><p>Autoregressive processes in generalized linear mixed effects regression models are convenient for the analysis of clinical trials that have a moderate to large number of binary repeated measurements, collected across a fixed set of structured time points, for each subject. However, much of the existing literature and methods for autoregressive processes on repeated binary measurements permit only one order and only one autoregressive process in the model. This limits the flexibility of the resulting generalized linear mixed effects regression model to fully capture the dynamics in the data, which can result in decreased power for testing treatment effects. Nested autoregressive structures enable more holistic modeling of clinical trials that can lead to increased power for testing effects.</p><p> </p><p>We introduce the Bayesian General Logistic Autoregressive Model (BGLAM) for the analysis of repeated binary measures in clinical trials. The BGLAM extends previous Bayesian models for binary repeated measures by accommodating flexible and nested autoregressive processes with non-informative priors. We describe methods for selecting the order of the autoregressive process in the BGLAM based on the Deviance Information Criterion (DIC) and marginal log-likelihood, and develop an importance sampling-weighted posterior predictive p-value to test for treatment effects in BGLAM. The frequentist properties of BGLAM compared to existing likelihood- and non-likelihood-based statistical models are evaluated by means of extensive simulation studies involving different data generation mechanisms.</p><p> </p><p>Two features of BGLAM that can limit its application in practice is the computational effort involved in executing it and the inability to integrate added heterogeneity across time in its autoregressive processes. We develop the Polya-Gamma Logistic Autoregressive Model (PGLAM) for addressing these limiting features of the BGLAM. This new model enables the integration of additional layers of variability through random effects and heterogeneity across time in nested autoregressive processes. Furthermore, PGLAM is computationally more efficient than BGLAM because it eliminates the need to use the complex types of samplers for truncated latent variables that is involved in the Markov Chain Monte Carlo algorithm for BGLAM.</p><p> </p><p><b>Data Generating Model for Phase III Clinical Trials With Intercurrent Events</b></p><p>Although clinical trials are designed with strict controls, inevitably complications will arise during the course of the trials. One significant type of complication is missing subject outcomes due to subject drop-out or nonadherence during the trial, which are referred to in general as intercurrent events. This complication can arise from, among other causes, adverse reactions, lack of efficacy of the assigned treatment, administrative reasons, and excess efficacy from the assigned treatment. Intercurrent events typically confound causal inferences on the effects of the treatments under investigation because the missingness that occurs as a result corresponds to a Missing Not at Random missing data mechanism, the pharmaceutical industry is increasingly focused on developing methods for obtaining valid causal inferences on the receipt of treatment in clinical trials with intercurrent events. However, it is extremely difficult to compare the frequentist properties and performance of these competing methods, as real-life clinical trial data cannot be easily accessed or shared, and as the different methods consider distinct assumptions for the underlying data generating mechanism in the clinical trial. We develop a novel simulation model for clinical trials with intercurrent events. Our simulator operates under the Rubin Causal Model. We implement the simulator by means of an R Shiny application. This app enables users to control patient compliance through different sources of discontinuity with varying functional trends, and understand the frequentist properties of treatment effect estimators obtained by different models for various estimands.</p>

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This research uses Bayesian analysis of fluorescence spectroscopy results to determine if wastewater from the Heber Valley Special Service District (HVSSD) lagoons in Midway, UT has seeped into the adjacent Provo River. This flow cannot be directly measured, but it is possible to use fluorescence spectroscopy to determine if there is seepage into the river.Fluorescence spectroscopy results of water samples obtained from HVSSD lagoons and from upstream and downstream in the Provo River were used to conduct this statistical analysis. The fluorescence 'fingerprints' for the upstream and lagoon samples were used to deconvolute the two sources in a downstream sample in a manner similar to the tools and methods discussed in the literature and used for source apportionment of air pollutants. The Bayesian statistical method employed presents a novel way of conducting source apportionment and identifying the existence of pollution.This research demonstrates that coupling fluorescence spectroscopy with Bayesian statistical methods allows researchers to determine the degree to which a water source has been contaminated by a pollution source. This research has applications in determining the affect sanitary wastewater lagoons and other lagoons have on an adjacent river due to groundwater seepage. The method used can be applied in scenarios where direct collection of hydrogeologic data is not possible. This research demonstrates that the Bayesian chemical mass balance model presented is a viable method of performing source apportionment.

This thesis investigates the use of Bayesian analysis upon an opponent¿s behaviour in order to determine the desired goals or strategy used by a given adversary. A terrain analysis approach utilising the A* algorithm is investigated, where a probability distribution between discrete behaviours of an opponent relative to a set of possible goals is generated. The Bayesian analysis of agent behaviour accurately determines the intended goal of an opponent agent, even when the opponent¿s actions are altered randomly. The environment of Poker is introduced and abstracted for ease of analysis. Bayes¿ theorem is used to generate an effective opponent model, categorizing behaviour according to its similarity with known styles of opponent. The accuracy of Bayes¿ rule yields a notable improvement in the performance of an agent once an opponent¿s style is understood. A hybrid of the Bayesian style predictor and a neuroevolutionary approach is shown to lead to effective dynamic play, in comparison to agents that do not use an opponent model. The use of recurrence in evolved networks is also shown to improve the performance and generalizability of an agent in a multiplayer environment. These strategies are then employed in the full-scale environment of Texas Hold¿em, where a betting round-based approach proves useful in determining and counteracting an opponent¿s play. It is shown that the use of opponent models, with the adaptive benefits of neuroevolution aid the performance of an agent, even when the behaviour of an opponent does not necessarily fit within the strict definitions of opponent ¿style¿. / Engineering and Physical Sciences Research Council (EPSRC)

Fit indices and fit measures commonly used to determine the accuracy and desirability of structural equation models are expected to be insensitive to nonlinearity in the data. This includes measures as ubiquitous as the CFI, TLI, RMSEA, SRMR, AIC, and BIC. Despite this, some software will report these measures when certain models are used. Consequently, some researchers may be led to use these fit measures without realizing the impropriety of the act. Alternative fit measures have been proposed, but these measures require further testing. As part of this thesis, a large simulation study was carried out to investigate alternative fit measures and to confirm whether the traditional measures are practically blind to nonlinearity in the data. The results of the simulation provide conclusive evidence that fit statistics and fit indices based on the chi-square distribution or the residual covariance matrix are entirely insensitive to nonlinearity. The posterior predictive p-value was also insensitive to nonlinearity. Only fit measures based on the structural residuals (i.e., HFI and R-squared) showed any sensitivity to nonlinearity. Of these, the R-squared was the only reliable measure of nonlinear model misspecification. This thesis shows that an effective strategy for determining whether a nonlinear model is preferable to a linear one involves using the R-squared to compare models that have been fit to the same data. An R-squared that is much larger for the nonlinear model than the linear model suggests that the linear model may be less desirable than the nonlinear model. The proposed method is intended to be supplementary to substantive theory. It is argued that any dependence on fit indices or fit statistics that places these measures on a higher pedestal than substantive theory will invariably lead to blindness on the part of the researcher. In other words, unwavering adherence to goodness-of-fit measures limits the researchers vision to what the measures themselves can detect.