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Random morphology and correlation functions
Published in Xi Frank Xu, Multiscale Theory of Composites and Random Media, 2018
where the subscript \ {i} indicates the full lattice excluding site i. The equivalence of Markov and Gibbs random field models, known as Hammersley-Clifford theorem (Hammersley & Clifford, 1971), connects spatial statistics to statistical physics. The set X becomes a Gibbs random field on and has Gibbs multivariate distribution P(x)=Z−1e−1TU(x)
Data Analysis
Published in Marian (Editor-in-Chief) Muste, Dennis A. Lyn, David M. Admiraal, Robert Ettema, Vladimir Nikora, Marcelo H. Garcia, Experimental Hydraulics: Methods, Instrumentation, Data Processing and Management, 2017
Marian (Editor-in-Chief) Muste, Dennis A. Lyn, David M. Admiraal, Robert Ettema, Vladimir Nikora, Marcelo H. Garcia
Various options for interpolating (or fitting – here no distinction will be made between the two) irregularly spaced data are available (and implemented in commercial software packages, such as Surfer or Tecplot or ArcGIS, or in more general purpose software such as R or MATLAB), and an overview is given in Eberly et al. (2004). Blanckaert and Graf (2001, 2004) applied nonlinear weighted splines to perform a least-squares surface fit of velocity data in a bend flow, and then examined terms involving spatial derivatives of fitted velocities in the relevant balance equations. Jamieson et al. (2013a, 2013b) applied kriging to interpolate velocity data, and then estimated vorticities from the interpolated data. The discussion in this section is restricted to the kriging technique (and specifically ordinary kriging), because, unlike other common techniques, its geostatistical basis provides error estimates. The theory of kriging is discussed in standard geostatistics or spatial statistics references such as Isaaks and Srivastava (1989), Cressie (1993), Olea (1999), and Webster and Oliver (2007).
Multiphase Flow in Porous Media
Published in Efstathios E. Michaelides, Clayton T. Crowe, John D. Schwarzkopf, Multiphase Flow Handbook, 2016
John R. Fanchi, John P. Seidle
where layer i has ow rate qi, net thickness qi, and permeability qi. is is derived from Darcy's law assuming the pressure di erence across each layer is the same, and the total ow rate is the sum of the rates in all layers. Equation 11.45 applies to both linear ow and radial ow. 11.3.3 Geostatistics A fundamental objective of the reservoir characterization process is to distribute rock properties throughout the volume of interest. Geostatistics can be used to characterize a reservoir by determining the statistical distribution of a rock property in space (Hirsche et al., 1997, Kelkar, 2000). Geostatistics, which is also known as spatial statistics, assumes that a spatially distributed property such as porosity is correlated from
Spatial analysis of road traffic accident hotspots: evaluation and validation of recent approaches using road safety audit
Published in Journal of Transportation Safety & Security, 2021
El-Said Mamdouh Mahmoud Zahran, Soon Jiann Tan, Eng Hie Angel Tan, Nurul Amirah 'Atiqah Binti Mohamad 'Asri Putra, Yok Hoe Yap, Ena Kartina Abdul Rahman
SANET-KDE and KDE + are network spatial analyses, but Getis-Ord Gi* is planar spatial analysis. Spatial statistical mapping is a key component to understanding the spatial and temporal occurrences of event points (Prasannakumar, Vijith, Charutha, & Geetha, 2011), such as RTA. Spatial statistics consist of techniques to describe and model spatial data such as aggregate event points. In this study, spatial statistical analysis for RTA can be performed using the Spatial Analyst extension in ArcMap 10.2. ArcMap is a powerful geospatial processing software that allows geographic information and corresponding attributes to be stored in layers of shapefiles and performs GIS analytical tasks according to user’s objectives. Before performing the Hotspot Analysis (Getis-Ord Gi*), spatial autocorrelation global Moran’s I test had to be conducted to investigate whether RTA points were organised in clusters of similar values.
Geographical patterns and effects of human and mechanical factors on road traffic crashes in Nigeria
Published in International Journal of Injury Control and Safety Promotion, 2020
Richard Adeleke, Tolulope Osayomi, Ayodeji E Iyanda
The data were analysed with the aid of spatial statistical techniques such as Global Moran’s I and spatial regression model. Other statistical techniques used include Pearson correlation and OLS regression. Spatial statistics is based on the assumption of the non-independence of observations; that is, nearby features are closely associated (Tobler, 1970). Consequently, spatial statistics are used in the analysis of spatial patterns, modelling spatial relationships and detecting spatial clusters (Osayomi, 2019). The Global Moran’s I was used to determine the nature of the geographical distribution of road traffic crashes, fatality and injury. Global Moran’s I value varies from −1 through 0 to +1. If Moran’s I value is near +1, it is an indication of a high positive spatial autocorrelation which also means that states with similar values of RTCs, fatality and injury are clustered over space. In contrast, a Moran’s I value near −1 is an indication of a high negative spatial autocorrelation, which means that states with dissimilar values of RTCs, fatality and injury are adjacent. A random pattern is depicted when the z scores are between −1.96 and +1.96 with a p value greater than 0.05. On the other hand, the pattern is clustered when the p value is less than 0.05.
Bayesian hierarchical modelling of basketball tracking data - a case study of spatial entropy and spatial effectiveness
Published in Journal of Sports Sciences, 2020
Wade Hobbs, Paul Pao-Yen Wu, Adam D. Gorman, Mitchell Mooney, Jonathan Freeston
Improved data collection technologies couples with a greater appreciation of the value of analytics has led to an increase in the utilisation of data in sports. The greatest advancements have been in spatio-temporal tracking data from global and local position systems, optical tracking systems and manual tracking methods. A range of methods are available to analyse spatio-temporal data, including Bayesian methods, however, there are many gaps in their application and development to sports data. Spatial statistics have been applied to great effect for spatio-temporal data in fields of research such as ecology, epidemiology and agriculture among others. Sports science and analytics research would benefit greatly from the application of these techniques to sports data sets.