2,095,118 research outputs found
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 locations
and time points with the possibility that . 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 is large relative to . 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 -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 Data Analysis
This handbook chapter provides an essential introduction to the field of
spatial econometrics, offering a comprehensive overview of techniques and
methodologies for analysing spatial data in the social sciences. Spatial
econometrics addresses the unique challenges posed by spatially dependent
observations, where spatial relationships among data points can significantly
impact statistical analyses. The chapter begins by exploring the fundamental
concepts of spatial dependence and spatial autocorrelation, and highlighting
their implications for traditional econometric models. It then introduces a
range of spatial econometric models, particularly spatial lag, spatial error,
and spatial lag of X models, illustrating how these models accommodate spatial
relationships and yield accurate and insightful results about the underlying
spatial processes. The chapter provides an intuitive understanding of these
models compare to each other. A practical example on London house prices
demonstrates the application of spatial econometrics, emphasising its relevance
in uncovering hidden spatial patterns, addressing endogeneity, and providing
robust estimates in the presence of spatial dependence
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.
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