High-SIR Transmission Capacity of Wireless Networks with General Fading and Node Distribution

In many wireless systems, interference is the main performance-limiting factor, and is primarily dictated by the locations of concurrent transmitters. In many earlier works, the locations of the transmitters is often modeled as a Poisson point process for analytical tractability. While analytically convenient, the PPP only accurately models networks whose nodes are placed independently and use ALOHA as the channel access protocol, which preserves the independence. Correlations between transmitter locations in non-Poisson networks, which model intelligent access protocols, makes the outage analysis extremely difficult. In this paper, we take an alternative approach and focus on an asymptotic regime where the density of interferers $\eta$ goes to 0. We prove for general node distributions and fading statistics that the success probability \p \sim 1-\gamma \eta^{\kappa} for $\eta \rightarrow 0$, and provide values of $\gamma$ and $\kappa$ for a number of important special cases. We show that $\kappa$ is lower bounded by 1 and upper bounded by a value that depends on the path loss exponent and the fading. This new analytical framework is then used to characterize the transmission capacity of a very general class of networks, defined as the maximum spatial density of active links given an outage constraint.Comment: Submitted to IEEE Trans. Info Theory special issu

Variance Approximation Approaches For The Local Pivotal Method

The problem of estimating the variance of the Horvitz-Thompson estimator of the population total when selecting a sample with unequal inclusion probabilities using the local pivotal method is discussed and explored. Samples are selected using unequal inclusion probabilities so that the estimates using the Horvitz-Thompson estimator will have smaller variance than for simple random samples. The local pivotal method is one sampling method which can select samples with unequal inclusion probability without replacement. The local pivotal method also balances on other available auxiliary information so that the variability in estimates can be reduced further. A promising variance estimator, bootstrap subsampling, which combines bootstrapping with rescaling to produce estimates of the variance is described and developed. This new variance estimator is compared to other estimators such as naive bootstrapping, the jackknife, the local neighborhood variance estimator of Stevens and Olsen, and the nearest neighbor estimator proposed by Grafstrom. For five example populations, we compare the performance of the variance estimators. The local neighborhood variance estimator performs best where it is appropriate. The nearest neighbor estimator performs second best and is more widely applicable. The bootstrap subsample variance estimator tends to underestimate the variance

Models and methods for computationally efficient analysis of large spatial and spatio-temporal data

With the development of technology, massive amounts of data are often observed at a large number of spatial locations (n). However, statistical analysis is usually not feasible or not computationally efficient for such large dataset. This is the so-called big n problem . The goal of this dissertation is to contribute solutions to the big n problem . The dissertation is devoted to computationally efficient methods and models for large spatial and spatio-temporal data. Several approximation methods to the big n problem are reviewed, and an extended autoregressive model, called the EAR model, is proposed as a parsimonious model that accounts for smoothness of a process collected over space. It is an extension of the Pettitt et a1. as well as Czado and Prokopenko parameterizations of the spatial conditional autoregressive (CAR) model. To complement the computational advantage, a structure removing orthonormal transformation named pre-whitening is described. This transformation is based on a singular value decomposition and results in the removal of spatial structure from the data. Circulant embedding technique further simplifies the calculation of eigenvalues and eigenvectors for the pre-whitening procedure. The EAR model is studied to have connections to the Matern class covariance structure in geostatistics as well as the integrated nested Laplace approximation (INLA) approach that is based on a stochastic partial differential equation (SPDE) framework. To model geostatistical data, a latent spatial Gaussian Markov random field (GMRF) with an EAR model prior is applied. The GMRF is defined on a fine grid and thus enables the posterior precision matrix to be diagonal through introducing a missing data scheme. This results in parameter estimation and spatial interpolation simultaneously under the Bayesian Markov chain Monte Carlo (MCMC) framework. The EAR model is naturally extended to spatio-temporal models. In particular, a spatio-temporal model with spatially varying temporal trend parameters is discussed

Co-localization Analysis of Bivariate Spatial Point Pattern

Spatial point pattern analysis investigates the localizations of random events in a defined spatial space usually conveyed in the form of images. Spatial distribution of two types of events observed in these images reflects their underlying interactions, which is the focus of co-localization analysis in spatial statistics. Malkusch et al. (Malkusch, et al., 2012) recently proposed the Coordinate-based Co-localization (CBC) method for co-localization analysis. However, the method did not incorporate edge corrections for point proportions and ignored their correlations over nested incremental observational regions. Hence, it yields false positive results for even complete spatial random distributions. In this research, we propose the new K(r) function Coordinate-based Colocalization (KCBC) method to quantify co-localization of two species by utilizing local bivariate Ripley\u27s K and Pearson’s Correlation Coefficient. Simulation studies are conducted to demonstrate the unbiasedness of the new method. An application to real life data was provided to illustrate its applicability

The influence of distance and level of service provision on antenatal care use in rural Zambia.

BACKGROUND: Antenatal care (ANC) presents important opportunities to reach women with crucial interventions. Studies on determinants of ANC use often focus on household and individual factors; few investigate the role of health service factors, partly due to lack of appropriate data. We assessed how distance to facilities and level of service provision at ANC facilities in Zambia influenced the number and timing of ANC visits and the quality of care received. METHODS AND FINDINGS: Using the 2005 Zambian national Health Facility Census, we classified ANC facilities according to the level of service provision. In a geographic information system, we linked the facility information to household data from the 2007 DHS to calculate straight-line distances. We performed multivariable multilevel logistic regression on 2405 rural births to investigate the influence of distance to care and of level of provision on three aspects of ANC use: attendance of at least four visits, visit in first trimester and receipt of quality ANC (4+ visits with skilled health worker and 8+ interventions). We found no effect of distance on timing of ANC or number of visits, and better level of provision at the closest facility was not associated with either earlier ANC attendance or higher number of visits. However, there was a strong influence of both distance to a facility, and level of provision at the closest ANC facility on the quality of ANC received; for each 10 km increase in distance, the odds of women receiving good quality ANC decreased by a quarter, while each increase in the level of provision category of the closest facility was associated with a 54% increase in the odds of receiving good quality ANC. CONCLUSIONS: To improve ANC quality received by mothers, efforts should focus on improving the level of services provided at ANC facilities and their accessibility

Illustrations and guidelines for selecting statistical methods for quantifying spatial pattern in ecological data

This paper aims to provide guidance to ecologists with limited experience in spatial analysis to help in their choice of techniques, It uses examples to compare methods of spatial analysis for ecological field data. A taxonomy of different data types is presented, including point- and area-referenced data, with and without attributes. Spatially and non-spatially explicit data are distinguished. The effects of sampling and other transformations that convert one data type to another are discussed; the possible loss of spatial information is considered. Techniques for analyzing spatial pattern, developed in plant ecology, animal ecology, landscape ecology, geostatistics and applied statistics are reviewed briefly and their overlap in methodology and philosophy noted. The techniques are categorized according to their output and the inferences that may be drawn from them, in a discursive style without formulae. Methods are compared for four case studies with field data covering a range of types. These are: 1) percentage cover of three shrubs along a line transect 2) locations and volume of a desert plant in a I ha area: 3) a remotely-sensed spectral index and elevation from 10(5) km(2) of a mountainous region; and 4) land cover from three rangeland types within 800 km2 of a coastal region. Initial approaches utilize mapping, frequency distributions and variance-mean indices. Analysis techniques we compare include: local quadrat variance, block, quadrat variance, correlograms, variograms, angular correlation, directional variograms, wavelets, SADIE, nearest neighbour methods, Ripley's L(t), and various landscape ecology metrics. Our advice to ecologists is to use simple visualization techniques for initial analysis, and subsequently to select methods that are appropriate for the data type and that answer their specific questions of interest, It is usually prudent to employ several different techniques

Spatial Data Mining Analytical Environment for Large Scale Geospatial Data

Nowadays, many applications are continuously generating large-scale geospatial data. Vehicle GPS tracking data, aerial surveillance drones, LiDAR (Light Detection and Ranging), world-wide spatial networks, and high resolution optical or Synthetic Aperture Radar imagery data all generate a huge amount of geospatial data. However, as data collection increases our ability to process this large-scale geospatial data in a flexible fashion is still limited. We propose a framework for processing and analyzing large-scale geospatial and environmental data using a “Big Data” infrastructure. Existing Big Data solutions do not include a specific mechanism to analyze large-scale geospatial data. In this work, we extend HBase with Spatial Index(R-Tree) and HDFS to support geospatial data and demonstrate its analytical use with some common geospatial data types and data mining technology provided by the R language. The resulting framework has a robust capability to analyze large-scale geospatial data using spatial data mining and making its outputs available to end users