Regularized Principal Component Analysis for Spatial Data

In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at $p$ locations and $n$ time points with the possibility that $p>n$. While principal component analysis (PCA) is commonly applied to find the dominant patterns, the eigenimages produced from PCA may exhibit patterns that are too noisy to be physically meaningful when $p$ is large relative to $n$. To obtain more precise estimates of eigenimages, we propose a regularization approach incorporating smoothness and sparseness of eigenimages, while accounting for their orthogonality. Our method allows data taken at irregularly spaced or sparse locations. In addition, the resulting optimization problem can be solved using the alternating direction method of multipliers, which is easy to implement, and applicable to a large spatial dataset. Furthermore, the estimated eigenfunctions provide a natural basis for representing the underlying spatial process in a spatial random-effects model, from which spatial covariance function estimation and spatial prediction can be efficiently performed using a regularized fixed-rank kriging method. Finally, the effectiveness of the proposed method is demonstrated by several numerical example

Exploratory spatial data analysis with GEOXP

GEOX is a computer package of Splus and Matlab routines implementing interactive graphics methods for exploring spatial data. We analyse a large data basis from the regional public health insurance agency concerning physicians'' activity in the Midi-Pyrénées region. We evaluate in particular heterogeneity and outliers in the density of physicians, their prescriptions per patient, salaries, number of visits per patient, etc.. We examine spatial dependencies of the main variables and thus locate spatial clusters. We attempt to explain the patterns of the prescription by some characteristics of the physicians together with the socio-economic characteristics of the counties using a spatial regression model with autocorrelated errors involving a hierarchical structure since these two sets of variables are known at a different level: physician level or county level.

A spatial likelihood analysis for MAGIC telescope data

Context. The increase in sensitivity of Imaging Atmospheric Cherenkov Telescopes (IACTs) has lead to numerous detections of extended $\gamma$-ray sources at TeV energies, sometimes of sizes comparable to the instrument's field of view (FoV). This creates a demand for advanced and flexible data analysis methods, able to extract source information by utilising the photon counts in the entire FoV. Aims. We present a new software package, "SkyPrism", aimed at performing 2D (3D if energy is considered) fits of IACT data, possibly containing multiple and extended sources, based on sky images binned in energy. Though the development of this package was focused on the analysis of data collected with the MAGIC telescopes, it can further be adapted to other instruments, such as the future Cherenkov Telescope Array (CTA). Methods. We have developed a set of tools that, apart from sky images (count maps), compute the instrument response functions (IRFs) of MAGIC (effective exposure throughout the FoV, point spread function (PSF), energy resolution and background shape), based on the input data, Monte-Carlo simulations and the pointing track of the telescopes. With this information, the presented package can perform a simultaneous maximum likelihood fit of source models of arbitrary morphology to the sky images providing energy spectra, detection significances, and upper limits. Results. We demonstrate that the SkyPrism tool accurately reconstructs the MAGIC PSF, on and off-axis performance as well as the underlying background. We further show that for a point source analysis with MAGIC's default observational settings, SkyPrism gives results compatible with those of the standard tools while being more flexible and widely applicable.Comment: 13 pages, 10 figure

Spatial Economic Analysis in Data-Rich Environments

Controlling for spatial effects in micro-economic studies of consumer and producer behavior necessitates a range of analytical modifications ranging from modest changes in data collection and the definition of variables to dramatic changes in the modeling of consumer and producer decision-making. This paper discusses conceptual, empirical, and data issues involved in modeling the spatial aspects of economic behavior in data rich environments. Attention is given to established and emerging agricultural economic applications of spatial data and spatial econometric methods at the micro-scale. Recent applications of individual and household data are featured, including models of land-use change at the urban-rural interface, agricultural land values, and technological change and technology adoption.Research Methods/ Statistical Methods, C21, Q10, Q12, Q15, Q56,

Bayesian spatial analysis of demographic survey data

In this paper we analyze the spatial patterns of the risk of unprotected sexual intercourse for Italian women during their initial experience with sexual intercourse. We rely on geo-referenced survey data from the Italian Fertility and Family Survey, and we use a Bayesian approach relying on weakly informative prior distributions. Our analyses are based on a logistic regression model with a multilevel structure. The spatial pattern uses an intrinsic Gaussian conditional autoregressive (CAR) error component. The complexity of such a model is best handled within a Bayesian framework, and statistical inference is carried out using Markov Chain Monte Carlo simulation. In contrast with previous analyses based on multilevel model, our approach avoids the restrictive assumption of independence between area effects. This model allows us to borrow strength from neighbors in order to obtain estimates for areas that may, on their own, have inadequate sample sizes. We show that substantial geographical variation exists within Italy (Southern Italy has higher risks of unprotected first-time sexual intercourse). The findings are robust with respect to the specification of the prior distribution. We argue that spatial analysis can give useful insights on unmet reproductive health needs.contraceptive use, FFS, hierarchical Bayesian modeling, Italy, Monte Carlo Markov Chain, multilevel statistical models, spatial statistical demography

Developments in the Analysis of Spatial Data

Disregarding spatial dependence can invalidate methods for analyzingcross-sectional and panel data. We discuss ongoing work on developingmethods that allow for, test for, or estimate, spatial dependence. Muchof the stress is on nonparametric and semiparametric methods.

Revisiting Guerry's data: Introducing spatial constraints in multivariate analysis

Standard multivariate analysis methods aim to identify and summarize the main structures in large data sets containing the description of a number of observations by several variables. In many cases, spatial information is also available for each observation, so that a map can be associated to the multivariate data set. Two main objectives are relevant in the analysis of spatial multivariate data: summarizing covariation structures and identifying spatial patterns. In practice, achieving both goals simultaneously is a statistical challenge, and a range of methods have been developed that offer trade-offs between these two objectives. In an applied context, this methodological question has been and remains a major issue in community ecology, where species assemblages (i.e., covariation between species abundances) are often driven by spatial processes (and thus exhibit spatial patterns). In this paper we review a variety of methods developed in community ecology to investigate multivariate spatial patterns. We present different ways of incorporating spatial constraints in multivariate analysis and illustrate these different approaches using the famous data set on moral statistics in France published by Andr\'{e}-Michel Guerry in 1833. We discuss and compare the properties of these different approaches both from a practical and theoretical viewpoint.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS356 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Assessing clustering methods for exploratory spatial data analysis

Exploratory spatial data analysis continues to be an important area of research. The use and application of clustering methods for the analysis of spatially referenced data is beginning to show some promise. However, a variety of clustering methods does exist. It is essential that a better understanding of these approaches in the geographic domain be pursued in terms of data requirements, computational efficiencies and inherent biases. This paper presents an initial attempt to demonstrate strengths and weaknesses of various clustering approaches for exploratory spatial data analysis.