In this thesis, we propose the predictive multicast polling scheme for medium access control in wireless networks with multipacket reception capability. We concentrate on the case in which the packet arrival process is general and the maximum queue size is finite but larger than one. We derive both analytical results and simulation results. We use the theory of discrete-time Markov chain to analyze the evolution of the system state. In addition, we propose to use Markov reward processes to calculate the throughput. Furthermore, we obtain the average system size, the packet blocking probability, and the average packet delay. The proposed analysis approach is applicable no matter whether perfect state information is available to the controller or not. We also use simulation results to justify the usage of the proposed approach. Our study shows that the system performance can be significantly improved with a few additional buffers in the queues. The proposed medium access control scheme can be used in the single-hop wireless local area networks and the multi-hop wireless mesh networks.

In the near future, the integration of GSM and GPRS services will bring the wireless personal communication networks into a new era. With the extreme growth in the number of users for contending limited resources, an efficient channel allocation scheme for GSM/GPRS users become very important. Currently, existing channel allocation schemes do not consider the various characteristics of traffic classes. Consequently, users can not obtain their optimal channel resources in delivering different types of traffic. In this thesis, a preemptive channel allocation mechanism is introduced for GSM/GPRS cellular networks. Based on the call requests, for different types of services, we classify the traffic into GSM, real-time GPRS and non-real-time GPRS. Two channel thresholds are defined. TGSM/GPRS is used to separate the channels between GSM and GPRS users, while TGPRS_rt is used to separate the channels between real-time and non-real-time GPRS users. Since the two thresholds can be dynamically adjusted based on the number of call requests, the channel utilization is increased and less resources are wasted. Note that in our proposed scheme, high-priority users¡]i.e., GSM handoff calls¡^can preempt the channels being used by low-priority users¡]i.e., non-real-time GPRS calls¡^. Hence, the call blocking probability of high-priority calls can be significantly reduced and their quality of services can be guaranteed as well. We build a 3-D Markov Chain mathematical model to analyze our proposed channel allocation schemes. The parameters of our interests include the call blocking probability, the average number of active calls, the average call completion rate and the overall channel utilization. To verify our mathematical results, we employ OPNET simulator to simulate the proposed schemes. Through the mathematical and simulation results, we have observed that with the preemptive channel allocation, the high-priority calls¡]i.e., GSM and real-time GPRS¡^can achieve relatively low blocking probability while slightly increasing the blocking probability of non-real-time GPRS calls. Besides, the overall channel utilization is greatly improved due to the appropriate channel allocation.

Univariate hierarchical Bayes models are being vigorously researched for use in disease mapping, engineering, geology, and ecology. This dissertation shows how the models can also be used to build modelbased risk maps for areabased roadway traffic crashes. Countylevel vehicle crash records and roadway data from Texas are used to illustrate the method. A potential extension that uses univariate hierarchical models to develop networkbased risk maps is also discussed. Several Bayesian multivariate spatial models for estimating the traffic crash rates from different types of crashes simultaneously are then developed. The specific class of spatial models considered is conditional autoregressive (CAR) model. The univariate CAR model is generalized for several multivariate cases. A general theorem for each case is provided to ensure that the posterior distribution is proper under improper and flat prior. The performance of various multivariate spatial models is compared using a Bayesian information criterion. The Markov chain Monte Carlo (MCMC) computational techniques are used for the model parameter estimation and statistical inference. These models are illustrated and compared again with the Texas crash data. There are many directions in which this study can be extended. This dissertation concludes with a short summary of this research and recommends several promising extensions.

<p>The aim of this thesis is to formulate and implement an algorithm that calculates the probability for two genes being orthologs, given a gene tree and a species tree. To do this, reconciliations between the gene tree and the species trees are used. A birth and death process is used to model the evolution, and used to calculate the orthology probability. The birth and death parameters are approximated with a Markov Chain Monte Carlo (MCMC). A MCMC framework for probability calculations of reconciliations written by Arvestad et al. (2003) is used. Rules for orthologous reconciliations are developed and implemented to calculate the probability for the reconciliations that have two genes as orthologs. The rules where integrated with the Arvestad et al. (2003) framework, and the algorithm was then validated and tested.</p>

This paper presents a spatial utility model of support for multiple political parties. The model includes a "valence" term, which I reparameterize to include both party competence and the voters' key sociodemographic concerns. The paper shows how this spatial utility model can be interpreted as a hierarchical model using data from the 2009 European Elections Study. I estimate this model via Bayesian Markov Chain Monte Carlo (MCMC) using a block Gibbs sampler and show that the model can capture broad European-wide trends while allowing for significant amounts of heterogeneity. This approach, however, which assumes a normal dependent variable, is only able to partially reproduce the data generating process. I show that the data generating process can be reproduced more accurately with an ordered probit model. Finally, I discuss trade-offs between parsimony and descriptive richness and other practical challenges that may be encountered when v building models of party support and make recommendations for capturing the best of both approaches. / text

We considered a non-centered parameterization of the standard random-effects model, which is based on the Cholesky decomposition of the variance-covariance matrix. The regression type structure of the non-centered parameterization allows to choose a simple, conditionally conjugate normal prior on the Cholesky factor. Based on the non-centered parameterization, we search for a parsimonious variance-covariance matrix by identifying the non-zero elements of the Cholesky factors using Bayesian variable selection methods. With this method we are able to learn from the data for each effect, whether it is random or not, and whether covariances among random effects are zero or not. An application in marketing shows a substantial reduction of the number of free elements of the variance-covariance matrix. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

We present a general framework for accelerating a large class of widely used Markov chain Monte Carlo (MCMC) algorithms. This dissertation demonstrates that MCMC inference can be accelerated in a model of parallel computation that uses speculation to predict and complete computational work ahead of when it is known to be useful. By exploiting fast, iterative approximations to the target density, we can speculatively evaluate many potential future steps of the chain in parallel. In Bayesian inference problems, this approach can accelerate sampling from the target distribution, without compromising exactness, by exploiting subsets of data. It takes advantage of whatever parallel resources are available, but produces results exactly equivalent to standard serial execution. In the initial burn-in phase of chain evaluation, it achieves speedup over serial evaluation that is close to linear in the number of available cores. / Engineering and Applied Sciences

Sequential Monte Carlo (SMC) and Forward Filtering Backward Sampling (FFBS) are the two most often seen algorithms for Bayesian state space models analysis. Various results regarding the applicability has been either claimed or shown. It is said that SMC would excel under nonlinear, non-Gaussian situations, and less computationally expansive. On the other hand, it has been shown that with techniques such as Grid approximation (Hore et al. 2010), FFBS based methods would do no worse, though still can be computationally expansive, but provide more exact information. The purpose of this report to compare the two methods with simulated data sets, and further explore whether there exist some clear criteria that may be used to determine a priori which methods would suit the study better. / text

While most statistical applications involve real numbers, some demand complex numbers. Statistical shape analysis is one such area. The complex Bingham distribution is utilized in the shape analysis of landmark data in two dimensions. Previous analysis of data arising from this distribution involved classical statistical techniques. In this report, a full Bayesian inference was carried out on the posterior distribution of the parameter matrix when data arise from a complex Bingham distribution. We utilized a Markov chain Monte Carlo algorithm to sample the posterior distribution of the parameters. A Metropolis-Hastings algorithm sampled the posterior conditional distribution of the eigenvalues while a successive conditional Monte Carlo sampler was used to sample the eigenvectors. The method was successfully verifi ed on simulated data, using both at and informative priors. / text

Item Response Theory (IRT) models are the basis of modern educational measurement. In order to increase testing efficiency, modern tests make ample use of groups of questions associated with a single stimulus (testlets). This violates the IRT assumption of local independence. However, a set of measurement models, testlet response theory (TRT), has been developed to address such dependency issues. This study investigates the effects of varying sample sizes and Markov Chain Monte Carlo burn-in chain lengths on the accuracy of estimation of a TRT model’s item and testlet parameters. The following outcome measures are examined: Descriptive statistics, Pearson product-moment correlations between known and estimated parameters, and indices of measurement effectiveness for final parameter estimates. / text