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In multiuser wireless networks, the base stations (BSs) rely on the channel state information (CSI) of the users to in order to perform user scheduling and downlink transmission. While the downlink channels can be easily estimated at all user terminals via a single broadcast, several key challenges are faced during uplink (feedback) transmission. Firstly, the noisy and fading feedback channels are usually unknown at the base station, and therefore, channel training is usually required from all users. Secondly, the amount of air-time required for feedback transmission grows linearly with the number of users. This domination of the network resources by feedback information leads to increased scheduling delay and outdated CSI at the BS. In this thesis, we tackle the above challenges and propose feedback reduction algorithms based on the theory of compressive sensing (CS). The proposed algorithms encompass both single and dual hop wireless networks, and; i) permit the BS to obtain CSI with acceptable recovery guarantees under substantially reduced feedback overhead, ii) are agnostic to the statistics of the feedback channels, and iii) utilize the apriori statistics of the additive noise to identify strong users. Numerical results show that the proposed algorithms are able to reduce the feedback overhead, improve detection at the BS, and achieve a sum-rate close to that obtained by noiseless dedicated feedback algorithms.

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I constructed a best estimate phylogeny based on congruence of multiple data sources. In recent years molecular data has been used both to construct phylogenies of taxonomic groups and to aid in the delimitation of new species. I generated and analyzed sequence data for forest spiny pocket mice (Genus Heteromys) for the mitochondrial gene cyt b (1143 bp) and two nuclear gene segments MYH2 (252 bp) and EN2 (189 bp). I used maximum parsimony and Bayesian analyses to infer relationships among species and to provide a framework for using a species delimitation method to investigate the possibility of multiple species within the widespread Heteromys desmarestianus. I found several well-supported lineages within the H.desmarestianus complex, including H. goldmani and H. oresterus. Incorporating karyotype and allozyme data from earlier studies, I found sufficient supporting evidence to justify maintaining H. goldmani and H. oresterus as species as well as identifying four lineages as candidate species. I present a revised taxonomic arrangement within the genus; the subgenus Heteromys should be divided into three species groups: anomalus (H. anomalus and H. australis), gaumeri (H. gaumeri), and desmarestianus (H. desmarestianus, H. goldmani, H. oresterus, and the four candidate species).

Computer models have become useful research tools in many disciplines. In many cases a researcher has access to data from a computer simulator and from a physical system. This research discusses Bayesian models that allow for the estimation of the discrepancy between the two data sources. We fit two models to data in the field of electrical engineering. Using this data we illustrate ways of modeling both a deterministic and a stochastic simulator when specific parametric assumptions can be made about the discrepancy term.

Test score distributions are used to make important instructional decisions about students. The test scores usually do not follow a normal distribution. In some cases, the scores appear to follow a bimodal distribution that can be modeled with a mixture of beta distributions. This bimodality may be due different levels of students' ability. The purpose of this study was to develop and apply statistical techniques for fitting beta mixtures and detecting bimodality in test score distributions. Maximum likelihood and Bayesian methods were used to estimate the five parameters of the beta mixture distribution for scores in four quizzes in a cell biology class at Brigham Young University. The mixing proportion was examined to draw conclusions about bimodality. We were successful in fitting the beta mixture to the data, but the methods were only partially successful in detecting bimodality.

In Wilderness Search and Rescue (WiSAR), the incident commander (IC) creates a probability distribution map of the likely location of the missing person. This map is important because it guides the IC in allocating search resources and coordinating efforts, but it often depends almost exclusively on prior experience and subjective judgment. We propose a Bayesian model that utilizes publicly available terrain features data to help model lost-person behaviors. This approach enables domain experts to encode uncertainty in their prior estimations and also make it possible to incorporate human-behavior data collected in the form of posterior distributions, which are used to build a first-order Markov transition matrix for generating a temporal, posterior predictive probability distribution map. The map can work as a base to be augmented by search and rescue workers to incorporate additional information. Using a Bayes Chi-squared test for goodness-of-fit, we show that the model fits a synthetic dataset well. This model also serves as a foundation of a larger framework that allows for easy expansion to incorporate additional factors such as season and weather conditions that affect the lost-person's behaviors. Once a probability distribution map is in place, areas with higher probabilities are searched first in order to find the missing person in the shortest expected time. When using a Unmanned Aerial Vehicle (UAV) to support search, the onboard video camera should cover as much of the important areas as possible within a set time. We explore several algorithms (with and without set destination) and describe some novel techniques in solving this path-planning problem and compare their performances against typical WiSAR scenarios. This problem is NP-hard, but our algorithms yield high quality solutions that approximate the optimal solution, making efficient use of the limited UAV flying time. The capability of planning a path with a set destination also enables the UAV operator to plan a path strategically while letting the UAV plan the path locally.

The goal of super-resolution is to increase not only the size of an image, but also its apparent resolution, making the result more plausible to human viewers. Many super-resolution methods do well at modest magnification factors, but even the best suffer from boundary and gradient artifacts at high magnification factors. This thesis presents Bayesian edge inference (BEI), a novel method grounded in Bayesian inference that does not suffer from these artifacts and remains competitive in published objective quality measures. BEI works by modeling the image capture process explicitly, including any downsampling, and modeling a fictional recapture process, which together allow principled control over blur. Scene modeling requires noncausal modeling within a causal framework, and an intuitive technique for that is given. Finally, BEI with trivial changes is shown to perform well on two tasks outside of its original domain—CCD demosaicing and inpainting—suggesting that the model generalizes well.