Vehicular communication is the enabling technology for the development of the intelligent transportation systems (ITS), which aims to improve the efficiency and safety of transportation. It can be used for a variety of useful applications such as adaptive traffic control, coordinated braking, emergency messaging, peer-to-peer networking for infotainment services and automatic toll collection etc... Accurate yet simple models for vehicular networks are required in order to understand and optimize their operation. For reliable communication between vehicles, the spectrum access is coordinated via carrier sense multiple access (CSMA) protocol. Existing models either use a simplified network abstraction and access control scheme for analysis or depend on simulation studies. Therefore it is important to develop an analytical model for CSMA coordinated communication between vehicles. In the first part of the thesis, stochastic geometry is exploited to develop a modeling framework for CSMA coordinated inter-vehicle communication (IVC) in a multi-lane highway scenario. The performance of IVC is studied in multi-lane highways taking into account the inter-lane separations and the number of traffic lanes and it is shown that for wide multi-lane highways, the line abstraction model that is widely used in literature loses accuracy and hence the analysis is not reliable. Since the analysis of CSMA in the vehicular setting makes the analysis intractable, an aggressive interference approximation and a conservative interference approximation is proposed for the probability of transmission success. These approximations are tight in the low traffic and high traffic densities respectively. In the subsequent part of the thesis, the developed model is extended to multi-hop IVC because several vehicular applications require going beyond the local communication and efficiently disseminate information across the roads via multi-hops. Two well-known greedy packet forwarding schemes are studied, that impose different tradeoffs between per-hop transmission success probability and forward packet progress, namely, the most forward with fixed radius (MFR) and the nearest with forward progress (NFP). In particular, a tractable and accurate modeling framework is developed to characterize the per-hop transmission success probability and the average forward progress for vehicular networks in a multi-lane highway setup. The developed model reveals the interplay between the spectrum sensing threshold of the CSMA protocol and the packet forwarding scheme. A new performance metric is defined, denoted as the aggregate packet progress (APP), which is a dimensionless quantity that captures the tradeoffs between the spatial frequency reuses efficiency, the per-hop transmission success probability, and the per-hop forward progress of the packets. To this end, in contrary to existing studies, the results show that with the proper manipulation of CSMA threshold, the MFR achieves the highest APP.

The availability of location estimates of mobile devices (MDs) is vital for several important applications such as law enforcement, disaster management, battlefield operations, vehicular communication, traffic safety, emergency response, and preemption. While global positioning system (GPS) is usually sufficient in outdoor clear sky conditions, its functionality is limited in urban canyons and indoor locations due to the absence of clear line-of-sight between the MD to be localized and a sufficient number of navigation satellites. In such scenarios, the ubiquitous nature of cellular networks makes them a natural choice for localization of MDs. Traditionally, localization in cellular networks has been studied using system level simulations by fixing base station (BS) geometries. However, with the increasing irregularity of the BS locations (especially due to capacity-driven small cell deployments), the system insights obtained by considering simple BS geometries may not carry over to real-world deployments. This necessitates the need to study localization performance under statistical (random) spatial models, which is the main theme of this work. In this thesis, we use powerful tools from stochastic geometry and point process theory to develop a tractable analytical model to study the localizability (ability to get a location fix) of an MD in single-tier and heterogeneous cellular networks (HetNets). More importantly, we study how availability of information about the location of proximate BSs at the MD impacts localizability. To this end, we derive tractable expressions, bounds, and approximations for the localizability probability of an MD. These expressions depend on several key system parameters, and can be used to infer valuable system insights. Using these expressions, we quantify the gains achieved in localizability of an MD when information about the location of proximate BSs is incorporated in the model. As expected, our results demonstrate that localizability improves with the increase in density of BS deployments. / Master of Science

Exact characterization and performance analysis of wireless networks should incorporate dependencies or correlations in space and time, i.e., study how the network performance varies spatially and temporally while having prior information about the performance at previous locations and time slots. This spatio-temporal correlation in wireless networks is usually characterized by studying metrics such as joint coverage probability at two spatial locations/time slots or spatio-temporal correlation coefficient. While developing models and analytical expressions for studying the two extreme cases of spatio-temoral correlation - i) uncorrelated scenario and ii) fully correlated scenario are easier, studying the intermediate case is non-trivial. In this thesis, we develop realistic and tractable analytical frameworks based on random spatial models (using tools from stochastic geometry) for modeling and analysis of correlation in cellular networks. With an ever increasing data demand, caching popular content in the storage of small cells (small cell caching) or the memory of user devices (device caching) is seen as a good alternative to offload demand from macro base stations and reduce backhaul loads. After providing generic results for traditional cellular networks, we study two applications exploiting spatio-temporal correlation in cache-enabled cellular networks. First, we determine the optimal cache content to be stored in the cache of a small cell network that maximizes the hit probability and minimizes the reception energy for the two extreme cases of correlation. Our results concretely demonstrate that the optimal cache contents are significantly different for the two correlation scenarios, thereby indicating the need of correlation-aware caching strategies. Second, we look at a distributed caching scenario in user devices and show that spatio-temporal correlation (user mobility) can be exploited to improve the network performance (in terms of coverage probability and local delay) significantly. / Master of Science

Determining the locations of devices in mobile ad-hoc networks (MANETs), wireless sensor networks (WSNs), and cellular networks has many important applications. In MANETs, which are useful in disaster recovery, rescue operations, and military communications, location information is used to enable location-aided routing and geodesic packet forwarding. In WSNs, whose applications include environmental monitoring (e.g., for precision agriculture) and asset tracking in warehouses, not only is location information useful for the self-organization of the network, but in addition, tying locations to the sensor observations is crucial for adding meaning to the sensed data. In cellular networks, location information is used to provide subscribers with location-based services in addition to providing public service answering points with potentially life-saving location information during emergency calls. These applications are largely not new, which is evidenced by the fact that the literature is quite rich with localization studies presented over the span of many years. Because of this, it may be surprising to learn that there is a lack of analyses concerning the fundamental factors impacting localization performance. Fundamentally, localization performance depends upon three factors: (i) the number of devices participating in the localization procedure, (ii) the locations of the participating devices, and (iii) the quality of the positioning observations gathered from the participating devices. For the most part, these factors cannot reasonably be considered deterministic. Instead, at any point in time, random effects within a network and its surroundings will determine these factors for individual positioning scenarios. Unfortunately, there are currently no analytical approaches for characterizing localization performance over these random factors. Instead, researchers either provide analytical results for a deterministic set of factors or use complex system-level simulations to obtain general performance insights. While the latter certainly averages over the random factors, the validity of the results is limited by the simulation assumptions. Any change in a network parameter requires running a new time-consuming simulation. In this dissertation, we address current deficiencies in several ways. We present a new model for tractably analyzing network localization fundamentals. This is demonstrated through fundamental analyses of hearability and geometry. Further, collaboration among non-reference devices has recently garnered increasing interest from the research community as a means to (i) improve positioning accuracy and (ii) improve positioning availability. We present fundamental analyses of both of these potential benefits. As a result of our work, we not only characterize several key performance metrics, we also demonstrate that there exist new tractable ways to analyze localization performance. / Ph. D.

Title: Cluster point processes in insurance mathematics Author: Veronika Veselá Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Zbyněk Pawlas, Ph.D. Abstract: In the present work we study point processes and their importance in insurance mathematics. With the help of cluster and marked point processes we can describe a model that considers times of claim occurence and times and hei- ghts of corresponding payments. We study two specific models which can be used to predict how much money is needed for claims which happened. The first model is chain ladder in the form of Mack's model. For this model we show chain ladder estimators of development factors, estimates of their variance and their proper- ties. We try to find one-step ahead prediction and multi-step ahead prediction, which we use for calculating prediction of reserves. We shortly review asymptotic properties of the estimators in Mack's model. The second model is the Poisson cluster model. Firstly we define this model and the variables entering the model. Then we devote attention to one-step ahead and multi-step ahead prediction. We also study prediction when some variables have specific distributions. Finally, we use both methods of prediction on simulated data and compare their average relative absolute errors....

<p>The modelling and analysis of complex stochastic systems with increasingly large data sets, state-spaces and parameters provides major stimulus to research in Bayesian nonparametric methods and Bayesian computation. This dissertation presents advances in both nonparametric modelling and statistical computation stimulated by challenging problems of analysis in complex spatio-temporal systems and core computational issues in model fitting and model assessment. The first part of the thesis, represented by chapters 2 to 4, concerns novel, nonparametric Bayesian mixture models for spatial point processes, with advances in modelling, computation and applications in biological contexts. Chapter 2 describes and develops models for spatial point processes in which the point outcomes are latent, where indirect observations related to the point outcomes are available, and in which the underlying spatial intensity functions are typically highly heterogenous. Spatial intensities of inhomogeneous Poisson processes are represented via flexible nonparametric Bayesian mixture models. Computational approaches are presented for this new class of spatial point process mixtures and extended to the context of unobserved point process outcomes. Two examples drawn from a central, motivating context, that of immunofluorescence histology analysis in biological studies generating high-resolution imaging data, demonstrate the modelling approach and computational methodology. Chapters 3 and 4 extend this framework to define a class of flexible Bayesian nonparametric models for inhomogeneous spatio-temporal point processes, adding dynamic models for underlying intensity patterns. Dependent Dirichlet process mixture models are introduced as core components of this new time-varying spatial model. Utilizing such nonparametric mixture models for the spatial process intensity functions allows the introduction of time variation via dynamic, state-space models for parameters characterizing the intensities. Bayesian inference and model-fitting is addressed via novel particle filtering ideas and methods. Illustrative simulation examples include studies in problems of extended target tracking and substantive data analysis in cell fluorescent microscopic imaging tracking problems.</p><p>The second part of the thesis, consisting of chapters 5 and chapter 6, concerns advances in computational methods for some core and generic Bayesian inferential problems. Chapter 5 develops a novel approach to estimation of upper and lower bounds for marginal likelihoods in Bayesian modelling using refinements of existing variational methods. Traditional variational approaches only provide lower bound estimation; this new lower/upper bound analysis is able to provide accurate and tight bounds in many problems, so facilitates more reliable computation for Bayesian model comparison while also providing a way to assess adequacy of variational densities as approximations to exact, intractable posteriors. The advances also include demonstration of the significant improvements that may be achieved in marginal likelihood estimation by marginalizing some parameters in the model. A distinct contribution to Bayesian computation is covered in Chapter 6. This concerns a generic framework for designing adaptive MCMC algorithms, emphasizing the adaptive Metropolized independence sampler and an effective adaptation strategy using a family of mixture distribution proposals. This work is coupled with development of a novel adaptive approach to computation in nonparametric modelling with large data sets; here a sequential learning approach is defined that iteratively utilizes smaller data subsets. Under the general framework of importance sampling based marginal likelihood computation, the proposed adaptive Monte Carlo method and sequential learning approach can facilitate improved accuracy in marginal likelihood computation. The approaches are exemplified in studies of both synthetic data examples, and in a real data analysis arising in astro-statistics.</p><p>Finally, chapter 7 summarizes the dissertation and discusses possible extensions of the specific modelling and computational innovations, as well as potential future work.</p> / Dissertation

The global effort to rehabilitate and restore destroyed mangrove forests is unable to keep up with the high mangrove deforestation rates which exceed the average pace of global deforestation by three to five times. Our knowledge of the underlying processes of mangrove forest regeneration is too limited in order to find suitable techniques for the restoration of degraded mangrove areas. The general objective of my dissertation was to improve mangrove restoration by understanding regeneration processes and local plant-plant interaction in a regenerating Avicennia germinans forest. The study was conducted in a high-shore mangrove forest area on the Ajuruteua peninsula, State of Para, Northern Brazil. The dwarf forest consisting of shrub-like trees is recovering from a stand-replacing event caused by a road construction in 1974 which interrupted the tidal inundation of the study area. Consequently, infrequent inundation and high porewater salinity limit tree growth and canopy closure. All trees and seedlings were stem-mapped in six 20 m x 20 m plots which were located along a tree density gradient. Moreover, height, crown extent, basal stem diameter of trees were measured. The area of herbaceous ground vegetation and wood debris were mapped as well. The mapped spatial distribution of trees, seedlings and covariates was studied using point pattern analysis and point process models, such as Gibbs and Thomas point process, in order to infer underlying ecological processes, such as seed dispersal, seedling establishment, tree recruitment and tree interaction. In the first study (chapter 2), I analyzed the influence of abiotic and biotic factors on the seedling establishment and tree recruitment of A. germinans during the recolonization of severely degraded mangrove sites using point process modeling. Most seedlings established adjacent to adult trees especially under their crown cover. Moreover, seedling density was higher within patches of the herbaceous salt-marsh plants Blutaparon portulacoides and Sesuvium portulacastrum than in uncovered areas. The higher density of recruited A. germinans trees in herb patches indicated that ground vegetation did not negatively influence tree development of A. germinans. In addition, tree recruitment occurred in clusters. Coarse wood debris had no apparent effect on either life stage. These results confirm that salt-marsh vegetation acts as the starting point for mangrove recolonization and indicate that the positive interaction among trees accelerates forest regeneration. In the second study (chapter 3), I analyzed how intraspecific interaction among A. germinans trees determines their growth and size under harsh environmental conditions. Interaction among a higher number of neighboring trees was positively related to the development of a focal tree. However, tree height, internode length and basal stem diameter were only positively associated in low-density forest stands (1.2 trees m-2) and not in forest stands of higher tree density (2.7 trees m-2). These results indicated a shift from facilitation, i.e. a positive effect of tree interaction, towards a balance between facilitation and competition. In the third study (chapter 4), I used point process modeling and the individual-based model mesoFON to disentangle the impact of regeneration and interaction processes on the spatial distribution of seedlings and trees. In this infrequently inundated area, propagules of A. germinans are only dispersed at a maximum distance of 3 m from their parent tree. Furthermore, there is no evidence that the following seedling establishment is influenced by trees. I was able to differentiate positive and negative tree interactions simulated by the mangrove model mesoFON regardless of dispersal processes based on static tree size information using the mark-correlation function. The results of this dissertation suggest that mangrove forest regeneration in degraded areas is a result of facilitative and not competitive interactions among mangrove trees, seedling and herbaceous vegetation. This has important implications for the restoration of degraded mangrove forest. Degraded mangrove areas are usually restored by planting a high number of evenly spaced seedlings. However, high costs constrain this approach to small areas. Assisting natural regeneration could be a less costly alternative. Herbaceous vegetation plays a crucial role in forest recolonization by entrapping propagules and possibly ameliorating harsh environmental conditions. So far only competition among mangrove trees has been considered during restoration. However, facilitative tree interactions could be utilized by planting seedling clusters in order to assist natural regeneration instead of planting seedlings evenly-spaced over large areas. This dissertation also showed that point pattern analysis and point process modeling can enable forest ecologists to describe the spatial distribution of trees as well as to infer underlying ecological processes.

Title: Models of Marked Point Processes Author: Ivan Héda Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Zbyněk Pawlas, Ph.D. Abstract: In the first part of the thesis, we present necessary theoretical basics as well as the definition of functional characteristics used for examination of marked point patterns. Second part is dedicated to review some known marking strategies. The core of the thesis lays in the study of intensity-marked point processes. General formula for the characteristics is proven for this marking strategy and general class of the models with analytically computable characteristics is introduced. This class generalizes some known models. Theoretical results are used for real data analysis in the last part of the thesis. Keywords: marked point process, marked log-Gaussian Cox process, intensity-marked point process 1

Wireless networks are increasingly interference-limited, which motivates the development of sophisticated interference management techniques. One recently discovered approach is interference alignment, which attains the maximum sum rate scaling (with signal-to-noise ratio) in many network configurations. Interference alignment is not yet well understood from an engineering perspective. Such design considerations include (i) partial rather than complete knowledge of channel state information, (ii) correlated channels, (iii) bursty packet-based network traffic that requires the frequent setup and tear down of sessions, and (iv) the spatial distribution and interaction of transmit/receive pairs. This dissertation aims to establish the benefits and limitations of interference alignment under these four considerations. The first contribution of this dissertation considers an isolated group of transmit/receiver pairs (a cluster) cooperating through interference alignment and derives the signal-to-interference-plus-noise ratio distribution at each receiver for each stream. This distribution is used to compare interference alignment to beamforming and spatial multiplexing (as examples of common transmission techniques) in terms of sum rate to identify potential switching points between them. This dissertation identifies such switching points and provides design recommendations based on severity of the correlation or the channel state information uncertainty. The second contribution considers transmitters that are not associated with any interference alignment cooperating group but want to use the channel. The goal is to retain the benefits of interference alignment amid interference from the out-of-cluster transmitters. This dissertation shows that when the out-of-cluster transmitters have enough antennas, they can access the channel without changing the performance of the interference alignment receivers. Furthermore, optimum transmit filters maximizing the sum rate of the out-of-cluster transmit/receive pairs are derived. When insufficient antennas exist at the out-of-cluster transmitters, several transmit filters that trade off complexity and sum rate performance are presented. The last contribution, in contrast to the first two, takes into account the impact of large scale fading and the spatial distribution of the transmit/receive pairs on interference alignment by deriving the transmission capacity in a decentralized clustered interference alignment network. Channel state information uncertainty and feedback overhead are considered and the optimum training period is derived. Transmission capacity of interference alignment is compared to spatial multiplexing to highlight the tradeoff between channel estimation accuracy and the inter-cluster interference; the closer the nodes to each other, the higher the channel estimation accuracy and the inter-cluster interference. / text

Part I presents a model for fingerprint matching using Bayesian alignment on unlabelled point sets. An efficient Monte Carlo algorithm is developed to calculate the marginal likelihood ratio between the hypothesis that an observed fingerprint and fingermark pair originate from the same finger and the hypothesis that they originate from different fingers. The model achieves good performance on the NIST-FBI fingerprint database of 258 matched fingerprint pairs, though the computed likelihood ratios are implausibly extreme due to oversimplification in our model. Part II moves to a more theoretical study of proper scoring rules. The chapters in this section are designed to be independent of each other. Chapter 9 uses proper scoring rules to calibrate the implausible likelihood ratios computed in Part I. Chapter 10 defines the class of compatible weighted proper scoring rules. Chapter 11 derives new results for the score matching estimator, which can quickly generate point estimates for a parametric model even when the normalization constant of the distribution is intractable. It is used to find an initial value for the iterative maximization procedure in §3.3. Appendix A describes a novel algorithm to efficiently sample from the posterior of a von Mises distribution. It is used within the fingerprint model sampling procedure described in §5.6. Appendix B includes various technical results which would otherwise disrupt the flow of the main dissertation.