假設二元反應曲線為簡單線性羅吉斯迴歸模型(Simple Linear Logistic Regression Model)，在樣本數為偶數的前題下，所謂的最佳D型設計(D-Optimal Design)是直接將半數的樣本點配置在第17.6個百分位數，而另一半則配置在第82.4個百分位數。很遺憾的是，這兩個位置在參數未知的情況下是無法決定的，因此逐次實驗設計法(Sequential Experimental Designs)在應用上就有其必要性。在大樣本的情況下，本文所探討的逐次實驗設計法在理論上具有良好的漸近最佳D型性質(Asymptotic D-Optimality)。尤其重要的是，這些特性並不會因為起始階段的配置不盡理想而消失，影響的只是收斂的快慢而已。但是在實際應用上，這些大樣本的理想性質卻不是我們關注的焦點。實驗步驟收斂速度的快慢，在小樣本的考慮下有決定性的重要性。基於這樣的考量，本文將提出三種起始階段設計的方法並透過模擬比較它們之間的優劣性。 / The D-optimal design is well known to be a two-point design for the simple linear logistic regression function model. Specif-ically , one half of the design points are allocated at the 17.6- th percentile, and the other half at the 82.4-th percentile. Since the locations of the two design points depend on the unknown parameters, the actual 2-locations can not be obtained. In order to dilemma, a sequential design is somehow necessary in practice. Sequential designs disscused in this context have some good properties that would not disappear even the initial stgae is not good enough under large sample size. The speed of converges of the sequential designs is influenced by the initial stage imposed under small sample size. Based on this, three initial stages will be provided in this study and will be compared through simulation conducted by C++ language.

A/B testing refers to the statistical procedure of experimental design and analysis to compare two treatments, A and B, applied to different testing subjects. It is widely used by technology companies such as Facebook, LinkedIn, and Netflix, to compare different algorithms, web-designs, and other online products and services. The subjects participating in these online A/B testing experiments are users who are connected in different scales of social networks. Two connected subjects are similar in terms of their social behaviors, education and financial background, and other demographic aspects. Hence, it is only natural to assume that their reactions to online products and services are related to their network adjacency. In this research, we propose to use the conditional autoregressive model (CAR) to present the network structure and include the network effects in the estimation and inference of the treatment effect. The following statistical designs are presented: D-optimal design for network A/B testing, a re-randomization experimental design approach for network A/B testing and covariate-assisted Bayesian sequential design for network A/B testing. The effectiveness of the proposed methods are shown through numerical results with synthetic networks and real social networks.

Fischer-Tropsch Synthesis (FTS) is a promising technology for the production of ultra-clean fuels and chemical feedstocks from biomass, coal, or natural gas. Iron catalysts are ideal for conversion of coal and biomass. However, precipitated iron catalysts used in slurry-bubble column reactors suffer from high attrition resulting in difficulty separating catalysts from product and increased slurry viscosity. Thus, development of an active and selective-supported iron catalyst to manage attrition is needed. This thesis focuses on the development of a supported iron catalyst and kinetic models of FTS on the catalyst using advanced statistical methods for experimental design and analysis. A high surface area alumina, modified by the addition of approximately 2 wt% lanthanum, was impregnated with approximately 20 wt% Fe and 1% Pt in a two step procedure. Approximately 10 wt% Fe and 0.5 wt% Pt was added in each step. The catalyst had a CO uptake of 702 μmol/g, extent of reduction of 69%, and was reduced at 450°C. The catalyst was stable over H2 partial pressures of 4-10 atm, CO partial pressures of 1-4 atm, and temperatures of 220-260°C. Weisz modulus values were less than 0.15. A Langmuir-Hinshelwood type rate expression, derived from a proposed FTS mechanism, was used with D-optimal criterion to develop experiments sequentially at 220°C and 239°C. Joint likelihood confidence regions for the rate expression parameters with respect to run number indicate rapid convergence to precise-parameter estimates. Difficulty controlling the process at the designed conditions and steep gradients around the D-optimal criterion resulted in consecutive runs having the same optimal condition. In these situations another process condition was chosen to avoid consecutive replication of the same process condition. A kinetic model which incorporated temperature effects was also regressed. Likelihood and bootstrap confidence intervals suggested that the model parameters were precise. Histograms and skewness statistics calculated from Bootstrap resampling show parameter-effect nonlinearities were small.

On-road vehicles are a major source of transportation carbon dioxide (CO2) greenhouse gas emissions in all the developed countries, and in many of the developing countries in the world. Similarly, several criteria air pollutants are associated with transportation, e.g., carbon monoxide (CO), nitrogen oxides (NOx), and particulate matter (PM). The need to accurately quantify transportation-related emissions from vehicles is essential. Transportation agencies and researchers in the past have estimated emissions using one average speed and volume on a long stretch of roadway. With MOVES, there is an opportunity for higher precision and accuracy. Integrating a microscopic traffic simulation model (such as VISSIM) with MOVES allows one to obtain precise and accurate emissions estimates. The new United States Environmental Protection Agency (USEPA) mobile source emissions model, MOVES2010a (MOVES) can estimate vehicle emissions on a second-by-second basis creating the opportunity to develop new software ―VIMIS 1.0‖ (VISSIM/MOVES Integration Software) to facilitate the integration process. This research presents a microscopic examination of five key transportation parameters (traffic volume, speed, truck percentage, road grade and temperature) on a 10-mile stretch of Interstate 4 (I- 4) test bed prototype; an urban limited access highway corridor in Orlando, Florida. iv The analysis was conducted utilizing VIMIS 1.0 and using an advanced custom design technique; D-Optimality and I-Optimality criteria, to identify active factors and to ensure precision in estimating the regression coefficients as well as the response variable. The analysis of the experiment identified the optimal settings of the key factors and resulted in the development of Micro-TEM (Microscopic Transportation Emissions MetaModel). The main purpose of Micro-TEM is to serve as a substitute model for predicting transportation emissions on limited access highways in lieu of running simulations using a traffic model and integrating the results in an emissions model to an acceptable degree of accuracy. Furthermore, significant emission rate reductions were observed from the experiment on the modeled corridor especially for speeds between 55 and 60 mph while maintaining up to 80% and 90% of the freeway‘s capacity. However, vehicle activity characterization in terms of speed was shown to have a significant impact on the emission estimation approach. Four different approaches were further examined to capture the environmental impacts of vehicular operations on the modeled test bed prototype. First, (at the most basic level), emissions were estimated for the entire 10-mile section ―by hand‖ using one average traffic volume and average speed. Then, three advanced levels of detail were studied using VISSIM/MOVES to analyze smaller links: average speeds and volumes (AVG), second-bysecond link driving schedules (LDS), and second-by-second operating mode distributions (OPMODE). This research analyzed how the various approaches affect predicted emissions of CO, NOx, PM and CO2. v The results demonstrated that obtaining accurate and comprehensive operating mode distributions on a second-by-second basis improves emission estimates. Specifically, emission rates were found to be highly sensitive to stop-and-go traffic and the associated driving cycles of acceleration, deceleration, frequent braking/coasting and idling. Using the AVG or LDS approach may overestimate or underestimate emissions, respectively, compared to an operating mode distribution approach. Additionally, model applications and mitigation scenarios were examined on the modeled corridor to evaluate the environmental impacts in terms of vehicular emissions and at the same time validate the developed model ―Micro-TEM‖. Mitigation scenarios included the future implementation of managed lanes (ML) along with the general use lanes (GUL) on the I-4 corridor, the currently implemented variable speed limits (VSL) scenario as well as a hypothetical restricted truck lane (RTL) scenario. Results of the mitigation scenarios showed an overall speed improvement on the corridor which resulted in overall reduction in emissions and emission rates when compared to the existing condition (EX) scenario and specifically on link by link basis for the RTL scenario. The proposed emission rate estimation process also can be extended to gridded emissions for ozone modeling, or to localized air quality dispersion modeling, where temporal and spatial resolution of emissions is essential to predict the concentration of pollutants near roadways