A wireless sensor network consists of a number of sensor devices and coordinator(s) or sink(s). A coordinator collects the sensed data from the sensor devices for further processing. In such networks, sensor devices are generally powered by batteries. Since wireless transmission of packets consumes significant amount of energy, it is important for a network to adopt a medium access control (MAC) technology which is energy efficient and satisfies the communication performance requirements. Carrier sense multiple access with collision avoidance (CSMA/CA), which is a popular access technique because of its simplicity, flexibility and robustness, suffers poor throughput and energy inefficiency performance in wireless sensor networks. On the other hand, time division multiple access (TDMA) is a collision free and delay bounded access technique but suffers from the scalability problem. For this reason, this thesis focuses on design and analysis of hybrid channel access schemes which combine the strengths of both the CSMA/CA and TDMA schemes. In a hybrid CSMA/CA-TDMA scheme, the use of the CSMA/CA period and the TDMA period can be optimized to enhance the communication performance in the network. If such a hybrid channel access scheme is not designed properly, high congestion during the CSMA/CA period and wastage of bandwidth during the TDMA period result in poor communication performance in terms of throughput and energy efficiency. To address this issue, distributed and centralized channel access schemes are proposed to regulate the activities (such as transmitting, receiving, idling and going into low power mode) of the sensor devices. This regulation during the CSMA/CA period and allocation of TDMA slots reduce traffic congestion and thus improve the network performance. In this thesis work, time slot allocation methods in hybrid CSMA/CA-TDMA schemes are also proposed and analyzed to improve the network performance. Finally, such hybrid CSMA/CA-TDMA schemes are used in a cellular layout model for the multihop wireless sensor network to mitigate the hidden terminal collision problem.

Statistical models have greatly improved our understanding of the pathogenesis of HIV-1 infection and guided for the treatment of AIDS patients and evaluation of antiretroviral (ARV) therapies. Although various statistical modeling and analysis methods have been applied for estimating the parameters of HIV dynamics via mixed-effects models, a common assumption of distribution is normal for random errors and random-effects. This assumption may lack the robustness against departures from normality so may lead misleading or biased inference. Moreover, some covariates such as CD4 cell count may be often measured with substantial errors. Bivariate clustered (correlated) data are also commonly encountered in HIV dynamic studies, in which the data set particularly exhibits skewness and heavy tails. In the literature, there has been considerable interest in, via tangible computation methods, comparing different proposed models related to HIV dynamics, accommodating skewness (in univariate) and covariate measurement errors, or considering skewness in multivariate outcomes observed in longitudinal studies. However, there have been limited studies that address these issues simultaneously. One way to incorporate skewness is to use a more general distribution family that can provide flexibility in distributional assumptions of random-effects and model random errors to produce robust parameter estimates. In this research, we developed Bayesian hierarchical models in which the skewness was incorporated by using skew-elliptical (SE) distribution and all of the inferences were carried out through Bayesian approach via Markov chain Monte Carlo (MCMC). Two real data set from HIV/AIDS clinical trial were used to illustrate the proposed models and methods. This dissertation explored three topics. First, with an SE distribution assumption, we compared models with different time-varying viral decay rate functions. The effect of skewness on the model fitting was also evaluated. The associations between the estimated decay rates based on the best fitted model and clinical related variables such as baseline HIV viral load, CD4 cell count and longterm response status were also evaluated. Second, by jointly modeling via a Bayesian approach, we simultaneously addressed the issues of outcome with skewness and a covariate process with measurement errors. We also investigated how estimated parameters were changed under linear, nonlinear and semiparametric mixed-effects models. Third, in order to accommodate individual clustering within subjects as well as the correlation between bivariate measurements such as CD4 and CD8 cell count measured during the ARV therapies, bivariate linear mixed-effects models with skewed distributions were investigated. Extended underlying normality assumption with SE distribution assumption was proposed. The impacts of different distributions in SE family on the model fit were also evaluated and compared. Real data sets from AIDS clinical trial studies were used to illustrate the proposed methodologies based on the three topics and compare various potential models with different distribution specifications. The results may be important for HIV/AIDS studies in providing guidance to better understand the virologic responses to antiretroviral treatment. Although this research is motivated by HIV/AIDS studies, the basic concepts of the methods developed here can have generally broader applications in other fields as long as the relevant technical specifications are met. In addition, the proposed methods can be easily implemented by using the publicly available WinBUGS package, and this makes our approach quite accessible to practicing statisticians in the fields.

This thesis develops hierarchical spatial models for the analysis of correlated and overdispersed count data based on the negative binomial distribution. Model development is motivated by a large scale study of fire frequency in British Columbia, conducted by the Pacific Forestry Service. Specific to our analysis, the main focus lies in examining the interaction between wildfire and forest insect outbreaks. In particular, we wish to relate the frequency of wildfire to the severity of mountain pine beetle (MPB) outbreaks in the province. There is a widespread belief that forest insect outbreaks lead to an increased frequency of wildfires; however, empirical evidence to date has been limited and thus a greater understanding of the association is required. This is critically important as British Columbia is currently experiencing a historically unprecedented MPB outbreak. We specify regression models for fire frequency incorporating random effects in a generalized linear mixed modeling framework. Within such a framework, both spatial correlation and extra-Poisson variation can be accommodated through random effects that are incorporated into the linear predictor of a generalized linear model. We consider a range of models, and conduct model selection and inference within the Bayesian framework with implementation based on Markov Chain Monte Carlo.

Technological improvements along with falling prices on photovoltaic (PV) panels and electric vehicles (EVs) suggest that they might become more common in the future. The introduction of distributed PV power production and EV charging has a considerable impact on the power system, in particular at the end-user in the electricity grid. In this PhD thesis PV power production, household electricity use and EV charging are investigated on different system levels. The methodologies used in this thesis are interdisciplinary but the main contributions are mathematical modeling, simulations and data analysis of these three components and their interactions. Models for estimating PV power production, household electricity use, EV charging and their combination are developed using data and stochastic modeling with Markov chains and probability distributions. Additionally, data on PV power production and EV charging from eight solar charging stations is analyzed. Results show that the clear-sky index for PV power production applications can be modeled via a bimodal Normal probability distribution, that household electricity use can be modeled via either Weibull or Log-normal probability distributions and that EV charging can be modeled by Bernoulli probability distributions. Complete models of PV power production, household electricity use and EV home-charging are developed with both Markov chain and probability distribution modeling. It is also shown that EV home-charging can be modeled as an extension to the Widén Markov chain model for generating synthetic household electricity use patterns. Analysis of measurements from solar charging stations show a wide variety of EV charging patterns. Additionally an alternative approach to modeling the clear-sky index is introduced and shown to give a generalized Ångström equation relating solar irradiation to the duration of bright sunshine. Analysis of the total power consumption/production patterns of PV power production, household electricity use and EV home-charging at the end-user in the grid highlights the dependency between the components, which quantifies the mismatch issue of distributed intermittent power production and consumption. At an aggregate level of households the level of mismatch is shown to be lower.

This work is an extension of the classical Cox-Ross-Rubinstein discrete time market model in which only one risky asset is considered. We introduce another risky asset into the model. Moreover, the random structure of the asset price sequence is generated by bivariate finite state Markov chain. Then, the interest rate varies over time as it is the function of generating sequences. We discuss how the model can be adapted to the real data. Finally, we illustrate sample implementations to give a better idea about the use of the model.

This thesis is concerned with the development of new mathematical models for the IEEE 802.11??s access mechanisms, with a particular focus on DCF and EDCA. Accurate mathematical models for the DCF and EDCA access mechanisms provide many benefits, such as improved performance analysis, easier network capacity planning, and robust network design. A feature that permeates the work presented in this thesis is the application of our new models to network environments where both saturated and non-saturated traffic sources are present. The scenario in which multiple traffic sources are present is more technically challenging, but provides for a more realistic setting. Our first contribution is the development of a new Markov model for non-saturated DCF in order to predict the network throughput. This model takes into account several details of the protocol that have been hitherto neglected. In addition, we apply a novel treatment of the packet service time within our model. We show how the inclusion of these effects provides more accurate predictions of network throughput than earlier works. Our second contribution is the development of a new analytical model for EDCA, again in order to predict network throughput. Our new EDCA model is based on a replacement of the normal AIFS parameter of EDCA with a new parameter more closely associated with DCF. This novel procedure allows EDCA to be viewed as a modified multi-mode version of DCF. Our third contribution is the simultaneous application of our new Markov models to both the non-saturated and the saturated regime. Hitherto, network throughput predictions for these regimes have required completely separate mathematical models. The convergence property of our model in the two regimes provides a new method to estimate the network capacity of the network. Our fourth contribution relates to predictions for the multimedia capacity of 802.11 networks. Our multimedia capacity analysis, which is based on modifications to our Markov model, is new in that it can be applied to a broad range of quality of service requirements. Finally, we highlight the use of our analysis in the context of emerging location-enabled networks.

The genealogy of a random sample of a population of organisms can be represented as a rooted binary tree. Population dynamics determine a distribution over sample genealogies. For large populations of constant size and in the absence of selection effects, the coalescent process of Kingman determines a suitable distribution. Neuhauser and Krone gave a stochastic model generalising the Kingman coalescent in a natural way to include the effects of selection. The model of Neuhauser and Krone determines a distribution over a class of graphs of randomly variable vertex number, known as ancestral selection graphs. Because vertices have associated scalar ages, realisations of the ancestral selection graph process have randomly variable dimensions. A Markov chain Monte Carlo method is used to simulate the posterior distribution for population parameters of interest. The state of the Markov chain Monte Carlo is a random graph, with random dimension and equilibrium distribution equal to the posterior distribution. The aim of the project is to determine if the data is informative of the selection parameter by fitting the model to synthetic data. / Foundation for Research Science and Technology Top Achiever Doctoral Scolarship

The genealogy of a random sample of a population of organisms can be represented as a rooted binary tree. Population dynamics determine a distribution over sample genealogies. For large populations of constant size and in the absence of selection effects, the coalescent process of Kingman determines a suitable distribution. Neuhauser and Krone gave a stochastic model generalising the Kingman coalescent in a natural way to include the effects of selection. The model of Neuhauser and Krone determines a distribution over a class of graphs of randomly variable vertex number, known as ancestral selection graphs. Because vertices have associated scalar ages, realisations of the ancestral selection graph process have randomly variable dimensions. A Markov chain Monte Carlo method is used to simulate the posterior distribution for population parameters of interest. The state of the Markov chain Monte Carlo is a random graph, with random dimension and equilibrium distribution equal to the posterior distribution. The aim of the project is to determine if the data is informative of the selection parameter by fitting the model to synthetic data. / Foundation for Research Science and Technology Top Achiever Doctoral Scolarship

The field of Machine Learning is concerned with the development of algorithms, models and techniques that solve challenging computational problems by learning from data representative of the problem (e.g. given a set of medical images previously classified by a human expert, build a model to predict unseen images as either benign or malignant). Many important real-world problems have been formulated as supervised learning problems. The assumption is that a data set is available containing the correct output (e.g. class label or target value) for each given data point. In many application domains, obtaining the correct outputs (labels) for data points is a costly and time-consuming task. This has provided the motivation for the development of Machine Learning techniques that attempt to minimize the number of labeled data points while maintaining good generalization performance on a given problem. Active Learning is one such class of techniques and is the focus of this thesis. Active Learning algorithms select or generate unlabeled data points to be labeled and use these points for learning. If successful, an Active Learning algorithm should be able to produce learning performance (e.g test set error) comparable to an equivalent supervised learner using fewer labeled data points. Theoretical, algorithmic and experimental Active Learning research has been conducted and a number of successful applications have been demonstrated. However, the scope of many of the experimental studies on Active Learning has been relatively small and there are very few large-scale experimental evaluations of Active Learning techniques. A significant amount of performance variability exists across Active Learning experimental results in the literature. Furthermore, the implementation details and effects of experimental factors have not been closely examined in empirical Active Learning research, creating some doubt over the strength and generality of conclusions that can be drawn from such results. The Active Learning model/system used in this thesis is the Optimal Active Learning algorithm framework with Gaussian Processes for regression problems (however, most of the research questions are of general interest in many other Active Learning scenarios). Experimental and implementation details of the Active Learning system used are described in detail, using a number of regression problems and datasets of different types. It is shown that the experimental results of the system are subject to significant variability across problem datasets. The hypothesis that experimental factors can account for this variability is then investigated. The results show the impact of sampling and sizes of the datasets used when generating experimental results. Furthermore, preliminary experimental results expose performance variability across various real-world regression problems. The results suggest that these experimental factors can (to a large extent) account for the variability observed in experimental results. A novel resampling technique for Optimal Active Learning, called '3-Sets Cross-Validation', is proposed as a practical solution to reduce experimental performance variability. Further results confirm the usefulness of the technique. The thesis then proposes an extension to the Optimal Active Learning framework, to perform learning via membership queries via a novel algorithm named MQOAL. The MQOAL algorithm employs the Metropolis-Hastings Markov chain Monte Carlo (MCMC) method to sample data points for query selection. Experimental results show that MQOAL provides comparable performance to the pool-based OAL learner, using a very generic, simple MCMC technique, and is robust to experimental factors related to the MCMC implementation. The possibility of making queries in batches is also explored experimentally, with results showing that while some performance degradation does occur, it is minimal for learning in small batch sizes, which is likely to be valuable in some real-world problem domains.

The genealogy of a random sample of a population of organisms can be represented as a rooted binary tree. Population dynamics determine a distribution over sample genealogies. For large populations of constant size and in the absence of selection effects, the coalescent process of Kingman determines a suitable distribution. Neuhauser and Krone gave a stochastic model generalising the Kingman coalescent in a natural way to include the effects of selection. The model of Neuhauser and Krone determines a distribution over a class of graphs of randomly variable vertex number, known as ancestral selection graphs. Because vertices have associated scalar ages, realisations of the ancestral selection graph process have randomly variable dimensions. A Markov chain Monte Carlo method is used to simulate the posterior distribution for population parameters of interest. The state of the Markov chain Monte Carlo is a random graph, with random dimension and equilibrium distribution equal to the posterior distribution. The aim of the project is to determine if the data is informative of the selection parameter by fitting the model to synthetic data. / Foundation for Research Science and Technology Top Achiever Doctoral Scolarship