Substance use data such as alcohol drinking often contain a high proportion of zeros. In studies examining the alcohol consumption in college students, for instance, many students may not drink in the studied period, resulting in a number of zeros. Zero-inflated continuous data, also called semi continuous data, typically consist of a mixture of a degenerate distribution at the origin (zero) and a right-skewed, continuous distribution for the positive values. Ignoring the extreme non-normality in semi-continuous data may lead to substantially biased estimates and inference. Longitudinal or repeated measures of semi-continuous data present special challenges in statistical inference because of the correlation tangled in the repeated measures on the same subject. Linear mixed-eects models (LMM) with normality assumption that is routinely used to analyze correlated continuous outcomes are inapplicable for analyzing semi-continuous outcome. Data transformation such as log transformation is typically used to correct the non-normality in data. However, log-transformed data, after the addition of a small constant to handle zeros, may not successfully approximate the normal distribution due to the spike caused by the zeros in the original observations. In addition, the reasons that data transformation should be avoided include: (i) transforming usually provides reduced information on an underlying data generation mechanism; (ii) data transformation causes diculty in regard to interpretation of the transformed scale; and (iii) it may cause re-transformation bias. Two-part mixed-eects models with one component modeling the probability of being zero and one modeling the intensity of nonzero values have been developed over the last ten years to analyze the longitudinal semi-continuous data. However, log transformation is still needed for the right-skewed nonzero continuous values in the two-part modeling. In this research, we developed Bayesian hierarchical models in which the extreme non-normality in the longitudinal semi-continuous data caused by the spike at zero and right skewness was accommodated using skew-elliptical (SE) distribution and all of the inferences were carried out through Bayesian approach via Markov chain Monte Carlo (MCMC). The substance abuse/dependence data, including alcohol abuse/dependence symptoms (AADS) data and marijuana abuse/dependence symptoms (MADS) data from a longitudinal observational study, were used to illustrate the proposed models and methods. This dissertation explored three topics: First, we presented one-part LMM with skew-normal (SN) distribution under Bayesian framework and applied it to AADS data. The association between AADS and gene serotonin transporter polymorphism (5-HTTLPR) and baseline covariates was analyzed. The results from the proposed model were compared with those from LMMs with normal, Gamma and LN distributional assumptions. Simulation studies were conducted to evaluate the performance of the proposed models. We concluded that the LMM with SN distribution not only provides the best model t based on Deviance Information Criterion (DIC), but also offers more intuitive and convenient interpretation of results, because it models the original scale of response variable. Second, we proposed a flexible two-part mixed-effects model with skew distributions including skew-t (ST) and SN distributions for the right-skewed nonzero values in Part II of model under a Bayesian framework. The proposed model is illustrated with the longitudinal AADS data and the results from models with ST, SN and normal distributions were compared under different random-effects structures. Simulation studies are conducted to evaluate the performance of the proposed models. Third, multivariate (bivariate) correlated semi-continuous data are also commonly encountered in clinical research. For instance, the alcohol use and marijuana use may be observed in the same subject and there might be underlying common factors to cause the dependence of alcohol and marijuana uses. There is very limited literature on multivariate analysis of semi-continuous data. We proposed a Bayesian approach to analyze bivariate semi-continuous outcomes by jointly modeling a logistic mixed-effects model on zero-inflation in either response and a bivariate linear mixed-effects model (BLMM) on the positive values through a correlated random-effects structure. Multivariate skew distributions including ST and SN distributions were used to relax the normality assumption in BLMM. The proposed models were illustrated with an application to the longitudinal AADS and MADS data. A simulation study was conducted to evaluate the performance of the proposed models.

The Carex nardina complex is a group of one to three species (C. nardina, C. hepburnii, C. stantonensis) and six taxa of unispicate sedges (Cyperaceae), the taxonomy of which has been controversial since the 1800s. As initial DNA phylogenies suggested that the complex was nested within Carex section Filifoliae and sister to C. elynoides, a species often confused with C. nardina and sympatric with it in the western North American Cordillera, analyses were conducted to determine whether C. hepburnii, C. stantonensis and other infraspecific taxa could be the result of hybridization. Morphometric and molecular analyses found no substantial evidence for hybridization and supported the recognition of no taxon beyond C. nardina. Consequently, this study concludes that the complex comprises a single variable species, Carex nardina, distributed throughout arctic North America south through the western Cordillera to New Mexico with a minor portion of its range in northeastern Russia, northwestern Scandinavia and Iceland.

This thesis addresses radiocarbon (C-14) dating of bioarcheological finds from Sandby borg, an iron-age ring fort on the east coast of the Baltic Sea island of Öland, Sweden. Archaeological evidence suggests that Sandby borg was used during the European migration period and that its main period of usage was terminated by an isolated incidence of inter-personal violence where the inhabitants were killed or abducted. Radiocarbon dating of individual archaeological finds from this period becomes imprecise due to fluctuations of C-14 ratios in the atmosphere during the period 420-530 AD. In the work presented here, Bayesian modelling, whereby multiple finds as well as chronological information from typology and stratigraphy are combined into a statistical model is deployed, together with an estimate of the percentage of maritime products in the diet of individuals subjected to C-14 dating. The outcome of this analysis suggests that the usage ranges from 410-537 AD (95.4% probability) and that the lethal attack took place between the years 532 and 558 AD (95.4% probability). This latter dating interval is about 40-60 years later than what has been suggested from previous studies. The reliability of the modified chronology and its consequences for our understanding of the Sandby borg site is discussed, and some future directions of research are proposed.

Do investors make bad decisions following the clock change? If so, there would be traces of such anomaly in market data. In this thesis, we investigate these traces focusing on the stock markets of the Visegrad Group, known to be pre- vailingly illiquid. We combine the most recent financial data with the ARIMA- GARCH framework while employing brand-new Bayesian techniques. Using several robustness checks, we show that such e ect cannot be traced in these markets. While we do not claim to challenge the seminal works in this field, we do support the evidence that the e ects of daylight saving policy do not pertain to less liquid markets. JEL Classification C11, G12, G14, G41 Keywords daylight saving time, market anomaly, Visegrad Group, Bayesian analysis Title Daylight Saving Time and Stock Market Re- turns: Evidence from the Visegrad Group

Background: The control of malaria in pregnancy remains a large challenge in Burkina Faso, despite the adoption of control measures known to be effective. Known effective programs include individual measures, such as intermittent preventive treatment during pregnancy, and the use of long lasting insecticide nets and daily supplementation of ferrous sulphate (200 mg) along with folic acid. Besides these measures, health programs that aim at enhancing the well-being of the population and improve maternal and child health have emerged, including results-based financing (in 2014), a project promoting health in 130 communities (implemented in 2015), and free health care (implemented in 2016). This thesis attempts to assess the effects of health programs on the space–time patterns of malaria (morbidity and mortality) through routinely collected data in pregnancy and explore the various prediction approaches to address challenges in routine health data reporting. Methods: We utilized a substantial range of data and applied advanced quantitative approaches while considering the specific distribution of the data. Our thesis is based on the valorization (analyses) of malaria surveillance data (aggregated by space and time units) recorded in the health information system of Burkina Faso between 2011 and 2019. These analyses also integrate environmental remote sensing data, data from periodic surveys, and data from other sources. These data were coupled into a database. After performing appropriate descriptive analyses considering the complexity of the data design, we performed spatio-temporal Bayesian modeling to determine areas with high risk and assess the effect of health programs on the space–time patterns of malaria incidence among pregnant women at the community-level; to explore an approach to estimate health facility readiness from survey data designed to be regionally representative (and then quantify the effect of this readiness on severe-malaria cases and case fatality); and to explore the prediction approaches used to address challenges in routine health data reporting, thereby supporting a malaria early warning system. Results: Our results show spatial and temporal heterogeneity and indicate that the annual incidence of malaria increased between 2013 and 2018, while the mortality rate decreased significantly. Some communities with a high malaria burden experienced a reduction in their risk through the deployment of the health programs mentioned above. The risk of a pregnant woman dying from severe malaria was 2.5 times higher in districts with low operational capacity. Finally, our thesis proposed an approach to respond to crisis situations that would affect data collection and could be used to set the target or provide early warnings for epidemics or other notifications. Conclusion: Our thesis provides useful tools for disease surveillance in developing countries to help optimize the scarce resources in malaria high burden areas. The results of our thesis could be used by the Ministry of Health to strengthen the capacity of existing surveillance tools and to develop rational strategies and/or new tools for monitoring malaria cases and associated deaths in communities. / Contexte :La lutte contre le paludisme pendant la grossesse reste un grand défi au Burkina Faso, malgré l'adoption de mesures de contrôle dont l'efficacité est reconnue. Les programmes dont l'efficacité est reconnue comprennent des mesures individuelles, telles que le traitement préventif intermittent pendant la grossesse, l'utilisation de moustiquaires imprégnées d'insecticide de longue durée et la supplémentation quotidienne en sulfate ferreux (200 mg) ainsi qu'en acide folique. Outre ces mesures, des programmes de santé visant à accroître le bien-être de la population et à améliorer la santé maternelle et infantile ont vu le jour, notamment le financement basé sur les résultats (en 2014), le projet de promotion de la santé dans 130 communes (mis en œuvre en 2015) et la gratuité des soins de santé (mise en œuvre en 2016). Cette thèse tente d'évaluer les effets des programmes de santé sur les caractéristiques spatio-temporelles du paludisme (morbidité et mortalité) par le biais de données de routine collectées pendant la grossesse et d'explorer les différentes approches de prévision pour relever les défis de la rapportage systématique des données de santé. Méthodes :Nous avons utilisé un large éventail de données et appliqué des approches quantitatives avancées tout en tenant compte de la distribution spécifique des données. Notre thèse est basée sur la valorisation (analyses) des données de surveillance du paludisme (agrégées par unités spatiales et temporelles) enregistrées dans le système d'information sanitaire du Burkina Faso entre 2011 et 2019. Ces analyses intègrent également des données de télédétection environnementale, des données issues d'enquêtes périodiques et des données provenant d'autres sources. Ces données ont été couplées pour constituer une base de données. Après avoir effectué des analyses descriptives appropriées en tenant compte de la complexité de la conception des données, nous avons procédé à une modélisation bayésienne spatio-temporelle pour déterminer les zones à haut risque et évaluer l'effet des programmes de santé sur les tendances spatio-temporelles de l'incidence du paludisme chez les femmes enceintes au niveau communautaire ;pour explorer une approche permettant d'estimer la capacité opérationnelle des établissements de santé à partir de données d'enquête conçues pour être représentatives au niveau régional (et ensuite quantifier l'effet de cette capacité opérationnelle sur les cas de paludisme grave et la mortalité) ;et pour explorer les approches de prévision utilisées pour relever les défis relatifs au rapportaga systématique des données de santé, pouvant aussi servir à un système d'alerte précoce du paludisme. Résultats :Nos résultats montrent une hétérogénéité spatiale et temporelle et indiquent que l'incidence annuelle du paludisme a augmenté entre 2013 et 2018, tandis que le taux de mortalité a diminué de manière significative. Certaines communes où la charge du paludisme est élevée ont connu une réduction de leur risque grâce au déploiement des programmes de santé mentionnés ci-dessus. Le risque qu'une femme enceinte meure d'un paludisme grave était 2,5 fois plus élevé dans les districts ayant une faible capacité opérationnelle. Enfin, notre thèse a proposé une approche pour répondre aux situations de crise qui affecterait la collecte de données et pourrait être utilisée pour fixer l'objectif ou fournir des alertes précoces pour les épidémies ou autres notifications. Conclusion :Notre thèse fournit des outils utiles pour la surveillance des maladies dans les pays en développement afin de contribuer à optimiser les ressources limitées dans les zones à forte incidence de paludisme. Les résultats de notre thèse pourraient être utilisés par le ministère de la santé pour renforcer la capacité des outils de surveillance existants et pour développer des stratégies rationnelles et/ou de nouveaux outils de surveillance des cas de paludisme et des décès associés dans les communautés. / Doctorat en Sciences de la santé Publique / info:eu-repo/semantics/nonPublished

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Point estimation of several association parameters in categorical data are presented. Typically, a constant is added to the frequency counts before the association measure is computed. We will study the accuracy of these adjusted point estimators based on frequentist and Bayesian methods respectively. In particular, amended estimators for the ratio of independent Poisson rates, relative risk, odds ratio, and the ratio of marginal binomial proportions will be examined in terms of bias and mean squared error.

<p>  </p> <p>Floods all over the world are one of the most common and devastating natural disasters for human society, and the flood risk is increasing recently due to more and more extreme climatic events. In the United States, one of the key resources that provide the flood risk information to the public is the Flood Insurance Rate Map (FIRM) administrated by the Federal Emergency Management Agency (FEMA) and the digitalized FIRMs have covered over 90% of the United States population so far. However, the uncertainty in the modeling process of FIRMs is rarely investigated. In this study, we use two of the widely used multi-model methods, the Bayesian Model Averaging (BMA) and the generalized likelihood uncertainty estimation (GLUE), to evaluate and reduce the impacts of various uncertainties with respect to modeling settings, evaluation metrics, and algorithm parameters on the flood modeling of FIRMs. Accordingly, three objectives of this study are to: (1) quantify the uncertainty in FEMA FIRMs by using BMA and Hierarchical BMA approaches; (2) investigate the inherent limitations and uncertainty in existing evaluation metrics of flood models; and (3) estimate the BMA parameters (weights and variances) using the Metropolis-Hastings (M-H) algorithm with multiple Markov Chains Monte Carlo (MCMC).</p> <p><br></p> <p>In the first objective, both the BMA and hierarchical BMA (HBMA) approaches are employed to quantify the uncertainty within the detailed FEMA models of the Deep River and the Saint Marys River in the State of Indiana based on water stage predictions from 150 HEC-RAS 1D unsteady flow model configurations that incorporate four uncertainty sources including bridges, channel roughness, floodplain roughness, and upstream flow input. Given the ensemble predictions and the observed water stage data in the training period, the BMA weight and the variance for each model member are obtained, and then the BMA prediction ability is validated for the observed data from the later period. The results indicate that the BMA prediction is more robust than both the original FEMA model and the ensemble mean. Furthermore, the HBMA framework explicitly shows the propagation of various uncertainty sources, and both the channel roughness and the upstream flow input have a larger impact on prediction variance than bridges. Hence, it provides insights for modelers into the relative impact of individual uncertainty sources in the flood modeling process. The results show that the probabilistic flood maps developed based on the BMA analysis could provide more reliable predictions than the deterministic FIRMs.</p> <p><br></p> <p>In the second objective, the inherent limitations and sampling uncertainty in several commonly used model evaluation metrics, namely, the Nash Sutcliffe efficiency (<em>NSE</em>), the Kling Gupta efficiency (<em>KGE</em>), and the coefficient of determination (<em>R</em>2), are investigated systematically, and hence the overall performance of flood models can be evaluated in a comprehensive way. These evaluation metrics are then applied to the 1D HEC-RAS models of six reaches located in the states of Indiana and Texas of the United States to quantify the uncertainty associated with the channel roughness and upstream flow input. The results show that the model performances based on the uniform and normal priors are comparable. The distributions of these evaluation metrics are significantly different for the flood model under different high-flow scenarios, and it further indicates that the metrics should be treated as random statistical variables given both aleatory and epistemic uncertainties in the modeling process. Additionally, the white-noise error in observations has the least impact on the evaluation metrics.</p> <p><br></p> <p>In the third objective, the Metropolis-Hastings (M-H) algorithm, which is one of the most widely used algorithms in the MCMC method, is proposed to estimate the BMA parameters (weights and variances), since the reliability of BMA parameters determines the accuracy of BMA predictions. However, the uncertainty in the BMA parameters with fixed values, which are usually obtained from the Expectation-Maximization (EM) algorithm, has not been adequately investigated in BMA-related applications over the past few decades. Both numerical experiments and two practical 1D HEC-RAS models in the states of Indiana and Texas of the United States are employed to examine the applicability of the M-H algorithm with multiple independent Markov chains. The results show that the BMA weights estimated from both algorithms are comparable, while the BMA variances obtained from the M-H MCMC algorithm are closer to the given variances in the numerical experiment. Overall, the MCMC approach with multiple chains can provide more information associated with the uncertainty of BMA parameters and its performance of water stage predictions is better than the default EM algorithm in terms of multiple evaluation metrics as well as algorithm flexibility.</p>

Alzheimer's disease (AD), the most common form of dementia, is a chronic neurodegenerative disease. The HECT domain and ankyrin repeat containing E3 ubiquitin protein ligase 1 (HACE1) gene is expressed in human brain and may play a role in the pathogenesis of neurodegenerative disorders. Till now, no previous study has reported the association of the HACE1 gene with the risk and age at onset (AAO) of AD; while few studies have checked the proportional hazards assumption in the survival analysis of AAO of AD using Cox proportional hazards model. In this study, we examined the associations of 14 single nucleotide polymorphisms (SNPs) in the HACE1 gene with the risk and the AAO of AD using 791 AD patients and 782 controls. Multiple logistic regression model identified one SNP (rs9499937 with p = 1.8×10) to be associated with the risk of AD. For survival analysis of AAO, both classic Cox regression model and Bayesian survival analysis using the Cox proportional hazards model were applied to examine the association of each SNP with the AAO. The hazards ratio (HR) with its 95% confidence interval (CI) was estimated. Survival analysis using the classic Cox regression model showed that 4 SNPs were significantly associated with the AAO (top SNP rs9499937 with HR=1.33, 95%CI=1.13-1.57, p=5.0×10). Bayesian Cox regression model showed similar but a slightly stronger associations (top SNP rs9499937 with HR=1.34, 95%CI=1.11-1.55) compared with the classic Cox regression model. Using an independent family-based sample, one SNP rs9486018 was associated with the risk of AD (p=0.0323) and the T-T-G haplotype from rs9786015, rs9486018 and rs4079063 showed associations with both the risk and AAO of AD (p=2.27×10 and 0.0487, respectively). The findings of this study provide first evidence that several genetic variants in the HACE1 gene were associated with the risk and AAO of AD.

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