Sampling design optimization for spatial functions

Olea, Ricardo A.

doi:10.1007/bf01029887

Cited by 184 publications

(110 citation statements)

References 2 publications

Supporting

Mentioning

108

Contrasting

Unclassified

Order By: Relevance

“…While it is difficult to extend this reasoning analytically to the sphere, studies by mathematicians (Saff & Kuijlaars, 1997) and GIS researchers (Kimerling, et al, 1999) both conclude that a hexagonal distribution has the highest International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XL-4/W2, 2013ISPRS WebMGS 2013& DMGIS 2013 November 2013, Xuzhou, Jiangsu, China Topics: Global Spatial Grid & Cloud-based Services degree of geometric regularity. On the plane a hexagonal distribution is the best known for estimating continuous spatial functions using kriging (Olea, 1984), and such a distribution is 13.4% more efficient than a square distribution of equivalent precision at sampling circularly bandlimited signals (Petersen & Middleton, 1962).…”

Section: The Limitations Of Fixed-width Floating Point Vector Locatiomentioning

confidence: 99%

On the Optimal Representation of Vector Location using Fixed-Width Multi-Precision Quantizers

Sahr

2013

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

View full text Add to dashboard Cite

ABSTRACT:Current generation geospatial applications primarily rely on location representations that were developed for the manipulation and display of planar maps of portions of the earth's surface. The next generation of digital earth applications will require fundamentally new technological approaches to location representation. Improvements in the efficiency of the representation of vector location can result in substantial performance increases. We examine the advantages and limitations of the most common current approach: as tuples of fixed-width floating point representations of real numbers, and identify a list of desirable design features for an optimal replacement system. These include the use of explicitly discrete integer indexes, the use of an optimal quantification scheme, and the ability to represent point locations at multiple precisions, including the capability to exactly represent key point locations, and the ability to encode multi-precision quantizations. We describe a class of planar systems that meet these criteria, which we call Central Place Indexing (CPI) systems. We then extend these systems to the sphere to provide a class of optimal known fixed-width geospatial vector location representation systems we call CPI43 systems.

show abstract

Section: The Limitations Of Fixed-width Floating Point Vector Locatiomentioning

confidence: 99%

On the Optimal Representation of Vector Location using Fixed-Width Multi-Precision Quantizers

Sahr

2013

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

View full text Add to dashboard Cite

show abstract

“…This approach minimizes the variability within a stratum, thus reducing the overall variability in the estimation [Olea, 1984;Matern, 1986]. When the underlying process is the result of a localized event, the stratified approach reduces the bias [McArthur, 1987].…”

Section: Stratification Of the Sampling Areamentioning

confidence: 99%

CO₂ emissions related to the Yellowstone volcanic system: 1. Developing a stratified adaptive cluster sampling plan

Boomer¹,

Werner²,

Brantley

2000

J. Geophys. Res.

View full text Add to dashboard Cite

Abstract. Statistical sampling theory offers several sampling designs that are wellsuited to geophysical research. Simple random sampling is the most commonly used formal methodology, in which the probability that any unit is sampled is known. Generally, units to be sampled are selected using a random number generator so that each unit has an equal chance of selection. In stratified sampling, the sampling frame is partitioned so that similar observed variable measurements are in each stratum. Systematic sampling attempts to capture the full variability within an area by obtaining samples at some predetermined interval. Adaptive cluster sampling is a relatively new methodology that allows additional units to be sampled, based on preceding sampling observations. The systematic adaptive sampling method applies adaptive cluster sampling to a systematic design. Selecting an appropriate design requires an understanding of the variability in the parameter of interest as well as the spatial covariance structure. This paper addresses such critical issues as sampling density, number of samples to collect, and assessment of the dimensions of a subregion to be sampled. While many researchers use the sampling designs presented herein, it is possible that inappropriate estimating equations were used. Formulae required to calculate unbiased, precise estimators for each of the designs are presented. The collection of CO2 flux degassing measurements from the Mud Volcano area, Yellowstone during the 1997 field season is used as a case study to outline the logical steps in selecting a sampling design. Although the case study used a stratified adaptive cluster sampling design, simpler designs can be developed based on the theory presented herein.

show abstract

“…In geostatistics, a hexagonal tessellation of sampling sites has a lower minimum average standard error, a lower maximum standard error, a larger screen effect (ability of sample points to minimize influence of points farther from the estimation point), and a smaller number of nearest neighbors for stable kriging, than a square tessellation (or any other pattern of sample points) (Olea 1984).…”

Section: Introductionmentioning

confidence: 99%

Topology matters: Network topology affects outcomes from community ecology neutral models

White

Kiester

2008

Computers, Environment and Urban Systems

View full text Add to dashboard Cite

Abstract. Topology affects outcomes of processes in planar networks. Hexagon tessellations have different performance than, and are often superior to, square tessellations in applications such as fluid dynamics, percolation theory, self-avoiding walks, survey sample design, and quantization. Hexagon tessellations and square tessellations using both von Neumann and Moore neighborhoods were examined as a network topology for neutral ecology community models, following the simulation approach of Graham Bell. These models, which assume identical life history and movement properties for each individual of each species, produce collective properties of communities, such as abundance distributions, range distributions, spatial variation in abundance, species-area curves, and spatial variation in species composition, that match many empirical patterns. The simulations in this study varied the dispersal rate but kept birth, death, and immigration rates constant. For these experiments, ending community populations, species richness, Shannon diversity, and Simpson diversity were clearly different for the different topologies, but the relationship between the topologies varied as the dispersal rate changed. Empirical distributions of the performance measures also showed clear differences among topologies. The interaction of topology with dispersal, spatial boundary effects, and other parameters of these models appears to be quite complex and warrants further research.

show abstract

Sampling design optimization for spatial functions

Cited by 184 publications

References 2 publications

On the Optimal Representation of Vector Location using Fixed-Width Multi-Precision Quantizers

On the Optimal Representation of Vector Location using Fixed-Width Multi-Precision Quantizers

CO₂ emissions related to the Yellowstone volcanic system: 1. Developing a stratified adaptive cluster sampling plan

Topology matters: Network topology affects outcomes from community ecology neutral models

Contact Info

Product

Resources

About

Sampling design optimization for spatial functions

Cited by 184 publications

References 2 publications

On the Optimal Representation of Vector Location using Fixed-Width Multi-Precision Quantizers

On the Optimal Representation of Vector Location using Fixed-Width Multi-Precision Quantizers

CO2 emissions related to the Yellowstone volcanic system: 1. Developing a stratified adaptive cluster sampling plan

Topology matters: Network topology affects outcomes from community ecology neutral models

Contact Info

Product

Resources

About

CO₂ emissions related to the Yellowstone volcanic system: 1. Developing a stratified adaptive cluster sampling plan