In this thesis, we explore a multi-indexed logistic regression (MILR) model, with particular emphasis given to its application to time series. MILR includes simple logistic regression (SLR) as a special case, and the hope is that it will in some instances also produce significantly better results. To motivate the development of MILR, we consider its application to the analysis of both simulated sine wave data and stock data. We looked at well-studied SLR and its application in the analysis of time series data. Using a more sophisticated representation of sequential data, we then detail the implementation of MILR. We compare their performance using forecast accuracy and an area under the curve score via simulated sine waves with various intensities of Gaussian noise and Standard & Poors 500 historical data. Overall, that MILR outperforms SLR is validated on both realistic and simulated data. Finally, some possible future directions of research are discussed.

The analysis of the error of perturbative series by comparing it to the exact solution is an important tool to understand the non-perturbative physics of statistical models. For some toy models, a new method can be used to calculate higher order weak coupling expansion and modified perturbation theory can be constructed. However, it is nontrivial to generalize the new method to understand the critical behavior of high dimensional spin and gauge models. Actually, it is a big challenge in both high energy physics and condensed matter physics to develop accurate and efficient numerical algorithms to solve these problems. In this thesis, one systematic way named tensor renormalization group method is discussed. The applications of the method to several spin and gauge models on a lattice are investigated. theoretically, the new method allows one to write an exact representation of the partition function of models with local interactions. E.g. O(N) models, Z2 gauge models and U(1) gauge models. Practically, by using controllable approximations, results in both finite volume and the thermodynamic limit can be obtained. Another advantage of the new method is that it is insensitive to sign problems for models with complex coupling and chemical potential. Through the new approach, the Fisher's zeros of the 2D O(2) model in the complex coupling plane can be calculated and the finite size scaling of the results agrees well with the Kosterlitz-Thouless assumption. Applying the method to the O(2) model with a chemical potential, new phase diagram of the models can be obtained. The structure of the tensor language may provide a new tool to understand phase transition properties in general.

In this dissertation, experimental investigations and theoretical studies on the stochastic matrix cracking evolution under static and fatigue loading in composite laminates with defects are presented. The presented work demonstrates a methodology that accounts for the statistically distributed defects in damage mechanics models for the assessment of the integrity of composites and for the structural design of composites. The experimental study deals with the mechanisms of the formation of a single crack on a micro-scale and the stochastic process for the multiplication of cracks on a macro-scale. The defects introduced by the manufacturing processes are found to have significant effect on the matrix cracking evolution. Influenced by the distributed defects, the initiation and multiplication of cracks evolve in a stochastic way. The experimental study on the in-plane shear stress finds the detrimental effect of the shear stress on the fatigue performance of composite laminates. Combined with the transverse tensile stress, the in-plane shear stress induces multiple inclined microcracks in the matrix, which enhance the initiation and propagation of the major matrix cracks. Based on the experimental investigations, a statistical model for the stochastic matrix cracking evolution on the macro-scale is developed. Simulations based on the statistical model yield accurate predictions for both static and fatigue loading compared to the experimental data. The Weibull distribution of the static strength is estimated by the statistical model by comparing against the experimental crack density data. The estimated Weibull distribution of the static strength provides an efficient approach to characterize the manufacturing quality of composite laminates. Compared to deterministic approaches, the Weibull distribution of the static strength provides comprehensive information of the strength property of composite laminates.

In countries with severe winters such like Canada, winter road maintenance (WRM) operations, such as plowing, salting and sanding, play an indispensible role in maintaining good road surface conditions and keeping roads safe. WRM is, however, also costly, both monetarily and environmentally. The substantial direct and indirect costs associated with WRM have stimulated significant interest in quantifying the safety and mobility benefits of winter road maintenance, such that systematic cost-benefit assessment can be performed. A number of studies have been initiated in the past decade to identify the links between winter road safety and factors related to weather, road, and maintenance operations. However, most of these studies have focused on the effects of adverse weather on road safety. Limited efforts have been devoted to the problem of quantifying the safety benefits of winter road maintenance under specific road weather conditions. Moreover, the joint effects of and complex interactions between road driving conditions, traffic and maintenance and their impact on traffic safety have rarely been studied. This research aims to determine the effect of WRM on road safety during snow storm events and develop models that can be used to quantify the safety benefit of alternative winter road maintenance policies, strategies and practices. Two integral aspects of collision risk were investigated, namely, collision frequency and severity. Collision frequency models were developed using winter storm collision data compiled for six winter seasons (2000 to 2006) for a total of 31 highway routes across Ontario. A comprehensive measure, namely, road surface condition index (RSI), was proposed to represent the road surface conditions during a variety of snow events. RSI was used as a surrogate measure to capture the effects of WRM. Other factors related to weather, traffic and road features were also accounted for in the analysis. Problems associated with data aggregation were also investigated. For this purpose, two different datasets were formed, namely, event-based data (EBD) which aggregates data by snow storm events and hourly based data (HBD) which includes hourly records of collision counts and other related factors. These two data sets of different aggregation levels were then used to investigate the effects of data aggregation and correlation (within – event) as well as to develop models for different purposes of benefit analyses. For EBD, Negative Binomial models and Generalized Negative Binomial models were calibrated whereas for HBD, Generalized Negative Binomial models and multilevel Poisson Lognormal models were calibrated. Generalized Negative Binomial models were found to best fit the data for both datasets. It was found that addition of site specific variables improves model fit. RSI and exposure were found significant for all the models and datasets. Weather factors such as visibility, wind speed, precipitation, and air temperature were also found to have statistically significant effects on collision frequency. All the models were consistent in terms of effects of different variables. The EBD models are useful to quantify the effect of different maintenance service standards and policies with limited information on the details of the weather events and traffic. On the other hand, HBD models have a higher level of reliability capable of providing more accurate estimates on road accidents. As a result, they are useful for determining the effects of different treatment operations. Several examples were employed to demonstrate the application of the developed models, such as quantifying the benefits of alternative maintenance operations and evaluating the effects of different service standards using safety as a performance measure. To enable a comprehensive risk analysis, collisions under both all-weather conditions and snow storm conditions over the six winter seasons were analyzed to identify the relationship between collision severity and various factors related to road weather and surface conditions, road characteristics, traffic, and vehicles etc., on collision severity. A multilevel modeling framework was introduced to capture the inherent hierarchy between collisions, vehicles and persons involved within the collision data. For each collision data set, three alternative severity models, namely, multinomial models, ordered logit models and binary logit models, were calibrated and compared. It was found that multilevel multinomial logit models were best fit to the data. Moreover issues related to different levels of aggregation were also discussed and results from occupant based data were found to be more reasonable and in line with general literature. Different individual, vehicle, environment and accident location factors were found to have a statistically significant effect on the injury severity levels. Contributing factors at the individual and vehicle levels include driver condition, driver sex, driver age, position in vehicle, use of safety device such as seat belt, vehicle type, vehicle age and vehicle condition. Roadway and environment factors include number of lanes, speed limit, road alignment, RSI/road surface condition, wind speed, and visibility. Other factors include light, and traffic volume. Two case studies were conducted to demonstrate the application of the developed models in conjunction with the accident frequency models for cost benefit analysis. This research was the first to investigate the direct link between road surface conditions and collisions at an operational level. It has been shown that the developed models are capable of evaluating alternative winter road maintenance policies and operations and assessing the safety benefit of a particular winter road maintenance strategy or decision. This research is also the first to conduct an in-depth analysis on the problem of winter road safety at a disaggregate level that captures detailed temporal variation (e.g., hourly and by storm event)) within small spatial aggregation units (road sections corresponding to actual patrol routes). The safety models developed from this research could be easily incorporated into a decision support tool for conducting what-if analysis of alternative winter road maintenance policies and methods. Moreover these models could provide a mechanism to estimate road safety level based on road surface as well as weather and traffic conditions and therefore could potentially be used for generating safety related information for travelers as part of a winter traffic management scheme. Directions for future work are also provided at the end of this document.

Thesis (Ph.D.)--University of Alabama at Birmingham, 2007. / Title from PDF title page (viewed on Feb. 19, 2010). Includes bibliographical references.

The sediment accumulation is an important characteristic in the ageing process of integrated constructed wetlands (ICW). Retained nutrient and other contaminants in wetland sediments have the potential to be remobilized and released to the overlying water column when environmental conditions change. In this study, mesocosms which filled with saturated sediments and planted with Phragmites australis and Agrostis stolonifera were set up to examine nutrient and other contaminants retention and/or release by wetland sediment and substrates. The effects of physico-chemical parameters on sediment-water contaminant exchange were also investigated through the application of multiple regression models, principal component analysis (PCA), redundancy analysis (RDA), and self-organizing map (SOM) model. The results demonstrated an average net release of chemical oxygen demand (COD), ammonianitrogen (NH3-N), nitrate-nitrogen (NO3-N) and molybdate reactive phosphorus (MRP) to the overlying water column, indicating that the ICW sediment and substrates acted as new contaminant sources. According to statistical analysis, electrical conductivity (EC) and redox potential (RP) values affected COD treatment efficiency. Chloride (Cl) concentration and RP value had an impact on NH3-N treatment performance. NO3-N removal was influenced by dissolved oxygen (DO) concentration and RP value. MRP treatment efficiency was related to DO concentration and EC value. The SOM model was selected as prediction tool to provide numerical estimations for the performance of ICW mesocosms. The model was validated, indicating that NH3-N, NO3-N, MRP, and COD treatment efficiencies could be predicted by input variables which are quick and cost-effective to measure. The SOM model can be seen as an appropriate method for monitoring the performance of mature ICWs. The type of vegetation played a minor role in releasing nutrients and other contaminants. However, the mesocosm planted with Phragmites australis outperformed the one planted with Agrostis stolonifera. No water reached bottom outlet of the mesocosm suggesting that there was little potential risk to contaminate groundwater. The clay liner and the biogeochemical processes taking place within sediments proved to be effective in preventing surface water from infiltration. Although no reduction in the overall performance has been observed for the full-scale ICW sites 7 and/or 11, this laboratory-scale study provided valuable warning signs regarding the loss of contaminant sequestration which may contribute to decline in wetland treatment performance over time. The impacts of hydraulic loading rate (HLR) and seasonal temperature fluctuations on contaminant removal efficiencies of a new ICW system receiving domestic wastewater were also assessed. The system showed good overall treatment performance in terms of effluent quality and removal efficiency. The influence of ICW removal efficiencies of the hydraulic loading rate, which was based on overall water balance, was negligible due to large footprint and multi-cellular configuration of the studied system. Relatively low temperature in autumns and winters resulted in decreased biological activities and lower contaminant removal efficiency. The long-term trends in nutrient removal have been investigated to five Wildfowl & Wetlands Trust constructed wetland systems. The results showed less effective removal even release of NO3-N, total oxidised nitrogen (TON), orthophosphate- phosphorus (PO4-P) and total phosphorus (TP) in many of the systems as a result of wetland aging and lack of sediment management.

In countries with severe winters such like Canada, winter road maintenance (WRM) operations, such as plowing, salting and sanding, play an indispensible role in maintaining good road surface conditions and keeping roads safe. WRM is, however, also costly, both monetarily and environmentally. The substantial direct and indirect costs associated with WRM have stimulated significant interest in quantifying the safety and mobility benefits of winter road maintenance, such that systematic cost-benefit assessment can be performed. A number of studies have been initiated in the past decade to identify the links between winter road safety and factors related to weather, road, and maintenance operations. However, most of these studies have focused on the effects of adverse weather on road safety. Limited efforts have been devoted to the problem of quantifying the safety benefits of winter road maintenance under specific road weather conditions. Moreover, the joint effects of and complex interactions between road driving conditions, traffic and maintenance and their impact on traffic safety have rarely been studied. This research aims to determine the effect of WRM on road safety during snow storm events and develop models that can be used to quantify the safety benefit of alternative winter road maintenance policies, strategies and practices. Two integral aspects of collision risk were investigated, namely, collision frequency and severity. Collision frequency models were developed using winter storm collision data compiled for six winter seasons (2000 to 2006) for a total of 31 highway routes across Ontario. A comprehensive measure, namely, road surface condition index (RSI), was proposed to represent the road surface conditions during a variety of snow events. RSI was used as a surrogate measure to capture the effects of WRM. Other factors related to weather, traffic and road features were also accounted for in the analysis. Problems associated with data aggregation were also investigated. For this purpose, two different datasets were formed, namely, event-based data (EBD) which aggregates data by snow storm events and hourly based data (HBD) which includes hourly records of collision counts and other related factors. These two data sets of different aggregation levels were then used to investigate the effects of data aggregation and correlation (within – event) as well as to develop models for different purposes of benefit analyses. For EBD, Negative Binomial models and Generalized Negative Binomial models were calibrated whereas for HBD, Generalized Negative Binomial models and multilevel Poisson Lognormal models were calibrated. Generalized Negative Binomial models were found to best fit the data for both datasets. It was found that addition of site specific variables improves model fit. RSI and exposure were found significant for all the models and datasets. Weather factors such as visibility, wind speed, precipitation, and air temperature were also found to have statistically significant effects on collision frequency. All the models were consistent in terms of effects of different variables. The EBD models are useful to quantify the effect of different maintenance service standards and policies with limited information on the details of the weather events and traffic. On the other hand, HBD models have a higher level of reliability capable of providing more accurate estimates on road accidents. As a result, they are useful for determining the effects of different treatment operations. Several examples were employed to demonstrate the application of the developed models, such as quantifying the benefits of alternative maintenance operations and evaluating the effects of different service standards using safety as a performance measure. To enable a comprehensive risk analysis, collisions under both all-weather conditions and snow storm conditions over the six winter seasons were analyzed to identify the relationship between collision severity and various factors related to road weather and surface conditions, road characteristics, traffic, and vehicles etc., on collision severity. A multilevel modeling framework was introduced to capture the inherent hierarchy between collisions, vehicles and persons involved within the collision data. For each collision data set, three alternative severity models, namely, multinomial models, ordered logit models and binary logit models, were calibrated and compared. It was found that multilevel multinomial logit models were best fit to the data. Moreover issues related to different levels of aggregation were also discussed and results from occupant based data were found to be more reasonable and in line with general literature. Different individual, vehicle, environment and accident location factors were found to have a statistically significant effect on the injury severity levels. Contributing factors at the individual and vehicle levels include driver condition, driver sex, driver age, position in vehicle, use of safety device such as seat belt, vehicle type, vehicle age and vehicle condition. Roadway and environment factors include number of lanes, speed limit, road alignment, RSI/road surface condition, wind speed, and visibility. Other factors include light, and traffic volume. Two case studies were conducted to demonstrate the application of the developed models in conjunction with the accident frequency models for cost benefit analysis. This research was the first to investigate the direct link between road surface conditions and collisions at an operational level. It has been shown that the developed models are capable of evaluating alternative winter road maintenance policies and operations and assessing the safety benefit of a particular winter road maintenance strategy or decision. This research is also the first to conduct an in-depth analysis on the problem of winter road safety at a disaggregate level that captures detailed temporal variation (e.g., hourly and by storm event)) within small spatial aggregation units (road sections corresponding to actual patrol routes). The safety models developed from this research could be easily incorporated into a decision support tool for conducting what-if analysis of alternative winter road maintenance policies and methods. Moreover these models could provide a mechanism to estimate road safety level based on road surface as well as weather and traffic conditions and therefore could potentially be used for generating safety related information for travelers as part of a winter traffic management scheme. Directions for future work are also provided at the end of this document.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 200-214).

This study examines the different skills necessary for PGA tour players to succeed at specific annual tournaments, in order to create a predictive model for DraftKings PGA contests. The model takes into account data from the PGA Tour ShotLink Intelligence Program. The predictive model is created each week based on past results from the specific tournament in question, with the hope of predicting a group of twenty-five players who should be successful based on their statistical profile. The results of the model are detailed in this paper, which covers the first nine weeks of the 2017 PGA Tour season, with a net profit of $45,070. Despite a positive profit there is not enough information to prove significance, so the model would need to be carried out for many more weeks to be conclusive. Ultimately, the study shows that each PGA Tour course is slightly different, which means certain players should be more successful at certain courses, which is valuable information for predicting future outcomes.

The extension of the CJS model to include individual, continuous, time-varying covariates relies on the estimation of covariate values on occasions on which individuals were not captured. Fitting this model in a Bayesian framework typically involves the implementation of a Markov chain Monte Carlo (MCMC) algorithm, such as a Gibbs sampler, to sample from the posterior distribution. For large data sets with many missing covariate values that must be estimated, this creates a computational issue, as each iteration of the MCMC algorithm requires sampling from the full conditional distributions of each missing covariate value. This dissertation examines two solutions to address this problem. First, I explore variational Bayesian algorithms, which derive inference from an approximation to the posterior distribution that can be fit quickly in many complex problems. Second, I consider an alternative approximation to the posterior distribution derived by truncating the individual capture histories in order to reduce the number of missing covariates that must be updated during the MCMC sampling algorithm. In both cases, the increased computational efficiency comes at the cost of producing approximate inferences. The variational Bayesian algorithms generally do not estimate the posterior variance very accurately and do not directly address the issues with estimating many missing covariate values. Meanwhile, the truncated CJS model provides a more significant improvement in computational efficiency while inflating the posterior variance as a result of discarding some of the data. Both approaches are evaluated via simulation studies and a large mark-recapture data set consisting of cliff swallow weights and capture histories.