Spatially stratified sampling using auxiliary information for geostatistical mapping

This paper presents a method of spatial sampling based on stratification by Local Moran’s I i calculated using auxiliary information. The sampling technique is compared to other design-based approaches including simple random sampling, systematic sampling on a regular grid, conditional Latin Hypercube sampling and stratified sampling based on auxiliary information, and is illustrated using two different spatial data sets. Each of the samples for the two data sets is interpolated using regression kriging to form a geostatistical map for their respective areas. The proposed technique is shown to be competitive in reproducing specific areas of interest with high accuracy.

A Novel Sub-Nyquist Fourier Transform Estimator Based on Alias-free Hybrid Stratified Sampling

This paper introduces a novel method of estimating theFourier transform of deterministic continuous-time signals from a finite number N of their nonuniformly spaced measurements. These samples, located at a mixture of deterministic and random time instants, are collected at sub-Nyquist rates since no constraints are imposed on either the bandwidth or the spectral support of the processed signal. It is shown that the proposed estimation approach converges uniformly for all frequencies at the rate N^−5 or faster. This implies that it significantly outperforms its alias-free-sampling-based predecessors, namely stratified and antithetical stratified estimates, which are shown to uniformly convergence at a rate of N^−1. Simulations are presented to demonstrate the superior performance and low complexity of the introduced technique.

Variance estimation with highly stratified sampling designs with unequal probabilities

It is common practice to design a survey with a large number of strata. However, in this case the usual techniques for variance estimation can be inaccurate. This paper proposes a variance estimator for estimators of totals. The method proposed can be implemented with standard statistical packages without any specific programming, as it involves simple techniques of estimation, such as regression fitting.

Stratified Sampling Applied to Estimation of the Volumetric Fraction of Alumina in Cast Metal Matrix Composites

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Latin hypercube sampling used in the calculation of the fracture probability

The paper proposes Latin hypercube sampling combined with the stratified sampling of variance reduction technique to calculate accurate fracture probability. In the compound sampling, the number of simulations is relatively small and the calculation error is satisfactory.

An Evaluation of the area stratification used for sampling tunas in the eastern Pacific Ocean and implications for estimating total annual catches

The Inter-American Tropical Tuna Commission (IATTC) staff has been sampling the size distributions of tunas in the eastern Pacific Ocean (EPO) since 1954, and the species composition of the catches since 2000. The IATTC staff use the data from the species composition samples, in conjunction with observer and/or logbook data, and unloading data from the canneries to estimate the total annual catches of yellowfin (Thunnus albacares), skipjack (Katsuwonus pelamis), and bigeye (Thunnus obesus) tunas. These sample data are collected based on a stratified sampling design. I propose an update of the stratification of the EPO into more homogenous areas in order to reduce the variance in the estimates of the total annual catches and incorporate the geographical shifts resulting from the expansion of the floating-object fishery during the 1990s. The sampling model used by the IATTC is a stratified two-stage (cluster) random sampling design with first stage units varying (unequal) in size. The strata are month, area, and set type. Wells, the first cluster stage, are selected to be sampled only if all of the fish were caught in the same month, same area, and same set type. Fish, the second cluster stage, are sampled for lengths, and independently, for species composition of the catch. The EPO is divided into 13 sampling areas, which were defined in 1968, based on the catch distributions of yellowfin and skipjack tunas. This area stratification does not reflect the multi-species, multi-set-type fishery of today. In order to define more homogenous areas, I used agglomerative cluster analysis to look for groupings of the size data and the catch and effort data for 2000–2006. I plotted the results from both datasets against the IATTC Sampling Areas, and then created new areas. I also used the results of the cluster analysis to update the substitution scheme for strata with catch, but no sample. I then calculated the total annual catch (and variance) by species by stratifying the data into new Proposed Sampling Areas and compared the results to those reported by the IATTC. Results showed that re-stratifying the areas produced smaller variances of the catch estimates for some species in some years, but the results were not significant.

A Comparison of Two Stratification Schemes Used in Sampling Canadian Atlantic Cod, Gadus morhua

Sampling is a key element in the assessment of any fish stock. It is often one of the most expensive activities of the management process; thus, improved efficiency can result in significant cost savings. In most cases a two-phase sampling strategy is employed. Two commonly used versions of such stratified random schemes were simulated using a test population based on Atlantic cod, Gadus morhua. A 1 otolith per 1 cm length frequency currently used for many flatfish and some smaller gadoids and a 3 otolith per 3 cm length frequency currently used for many of the larger gadoids. No difference was detected in the age composition or mean length at age for either scheme; however, 10 percent fewer otoliths were collected in 1 for 1 sampling than 3 for 3. There was an improvement of between 30 and 60 percent in the coefficient of variation of the estimated catch numbers at age using the 1 for 1 compared with the 3 for 3 stratified sampling. For these reasons and other operational considerations, the 1 for 1 stratified random design of sampling appears to be superior.

Uncertainties in annual riverine phosphorus load estimation: Impact of load estimation methodology, sampling frequency, baseflow index and catchment population density

Models developed to identify the rates and origins of nutrient export from land to stream require an accurate assessment of the nutrient load present in the water body in order to calibrate model parameters and structure. These data are rarely available at a representative scale and in an appropriate chemical form except in research catchments. Observational errors associated with nutrient load estimates based on these data lead to a high degree of uncertainty in modelling and nutrient budgeting studies. Here, daily paired instantaneous P and flow data for 17 UK research catchments covering a total of 39 water years (WY) have been used to explore the nature and extent of the observational error associated with nutrient flux estimates based on partial fractions and infrequent sampling. The daily records were artificially decimated to create 7 stratified sampling records, 7 weekly records, and 30 monthly records from each WY and catchment. These were used to evaluate the impact of sampling frequency on load estimate uncertainty. The analysis underlines the high uncertainty of load estimates based on monthly data and individual P fractions rather than total P. Catchments with a high baseflow index and/or low population density were found to return a lower RMSE on load estimates when sampled infrequently than those with a tow baseflow index and high population density. Catchment size was not shown to be important, though a limitation of this study is that daily records may fail to capture the full range of P export behaviour in smaller catchments with flashy hydrographs, leading to an underestimate of uncertainty in Load estimates for such catchments. Further analysis of sub-daily records is needed to investigate this fully. Here, recommendations are given on load estimation methodologies for different catchment types sampled at different frequencies, and the ways in which this analysis can be used to identify observational error and uncertainty for model calibration and nutrient budgeting studies. (c) 2006 Elsevier B.V. All rights reserved.

Parallel Monte Carlo sampling scheme for sphere and hemisphere

The sampling of certain solid angle is a fundamental operation in realistic image synthesis, where the rendering equation describing the light propagation in closed domains is solved. Monte Carlo methods for solving the rendering equation use sampling of the solid angle subtended by unit hemisphere or unit sphere in order to perform the numerical integration of the rendering equation. In this work we consider the problem for generation of uniformly distributed random samples over hemisphere and sphere. Our aim is to construct and study the parallel sampling scheme for hemisphere and sphere. First we apply the symmetry property for partitioning of hemisphere and sphere. The domain of solid angle subtended by a hemisphere is divided into a number of equal sub-domains. Each sub-domain represents solid angle subtended by orthogonal spherical triangle with fixed vertices and computable parameters. Then we introduce two new algorithms for sampling of orthogonal spherical triangles. Both algorithms are based on a transformation of the unit square. Similarly to the Arvo's algorithm for sampling of arbitrary spherical triangle the suggested algorithms accommodate the stratified sampling. We derive the necessary transformations for the algorithms. The first sampling algorithm generates a sample by mapping of the unit square onto orthogonal spherical triangle. The second algorithm directly compute the unit radius vector of a sampling point inside to the orthogonal spherical triangle. The sampling of total hemisphere and sphere is performed in parallel for all sub-domains simultaneously by using the symmetry property of partitioning. The applicability of the corresponding parallel sampling scheme for Monte Carlo and Quasi-D/lonte Carlo solving of rendering equation is discussed.

Sampling density and proportion for the characterization of the variability of Oxisol attributes on different materials

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Spatial methods for plot-based sampling of wildlife populations

Classical sampling methods can be used to estimate the mean of a finite or infinite population. Block kriging also estimates the mean, but of an infinite population in a continuous spatial domain. In this paper, I consider a finite population version of block kriging (FPBK) for plot-based sampling. The data are assumed to come from a spatial stochastic process. Minimizing mean-squared-prediction errors yields best linear unbiased predictions that are a finite population version of block kriging. FPBK has versions comparable to simple random sampling and stratified sampling, and includes the general linear model. This method has been tested for several years for moose surveys in Alaska, and an example is given where results are compared to stratified random sampling. In general, assuming a spatial model gives three main advantages over classical sampling: (1) FPBK is usually more precise than simple or stratified random sampling, (2) FPBK allows small area estimation, and (3) FPBK allows nonrandom sampling designs.

GMM Based Inference with Standard Stratified Samples when the Aggregate Shares are Known

We show how to do efficient moment based inference using the generalized method of moments (GMM) when data is collected by standard stratified sampling and the maintained assumption is that the aggregate shares are known.

Moment Based Inference with Stratified Data

Many datasets used by economists and other social scientists are collected by stratified sampling. The sampling scheme used to collect the data induces a probability distribution on the observed sample that differs from the target or underlying distribution for which inference is to be made. If this effect is not taken into account, subsequent statistical inference can be seriously biased. This paper shows how to do efficient semiparametric inference in moment restriction models when data from the target population is collected by three widely used sampling schemes: variable probability sampling, multinomial sampling, and standard stratified sampling.

Incorporating uncertainty in environmental models informed by imagery

In this thesis, the issue of incorporating uncertainty for environmental modelling informed by imagery is explored by considering uncertainty in deterministic modelling, measurement uncertainty and uncertainty in image composition. Incorporating uncertainty in deterministic modelling is extended for use with imagery using the Bayesian melding approach. In the application presented, slope steepness is shown to be the main contributor to total uncertainty in the Revised Universal Soil Loss Equation. A spatial sampling procedure is also proposed to assist in implementing Bayesian melding given the increased data size with models informed by imagery. Measurement error models are another approach to incorporating uncertainty when data is informed by imagery. These models for measurement uncertainty, considered in a Bayesian conditional independence framework, are applied to ecological data generated from imagery. The models are shown to be appropriate and useful in certain situations. Measurement uncertainty is also considered in the context of change detection when two images are not co-registered. An approach for detecting change in two successive images is proposed that is not affected by registration. The procedure uses the Kolmogorov-Smirnov test on homogeneous segments of an image to detect change, with the homogeneous segments determined using a Bayesian mixture model of pixel values. Using the mixture model to segment an image also allows for uncertainty in the composition of an image. This thesis concludes by comparing several different Bayesian image segmentation approaches that allow for uncertainty regarding the allocation of pixels to different ground components. Each segmentation approach is applied to a data set of chlorophyll values and shown to have different benefits and drawbacks depending on the aims of the analysis.

How can soil monitoring networks be used to improve predictions of organic carbon pool dynamics and CO2 fluxes in agricultural soils?

Abstract As regional and continental carbon balances of terrestrial ecosystems become available, it becomes clear that the soils are the largest source of uncertainty. Repeated inventories of soil organic carbon (SOC) organized in soil monitoring networks (SMN) are being implemented in a number of countries. This paper reviews the concepts and design of SMNs in ten countries, and discusses the contribution of such networks to reducing the uncertainty of soil carbon balances. Some SMNs are designed to estimate country-specific land use or management effects on SOC stocks, while others collect soil carbon and ancillary data to provide a nationally consistent assessment of soil carbon condition across the major land-use/soil type combinations. The former use a single sampling campaign of paired sites, while for the latter both systematic (usually grid based) and stratified repeated sampling campaigns (5–10 years interval) are used with densities of one site per 10–1,040 km². For paired sites, multiple samples at each site are taken in order to allow statistical analysis, while for the single sites, composite samples are taken. In both cases, fixed depth increments together with samples for bulk density and stone content are recommended. Samples should be archived to allow for re-measurement purposes using updated techniques. Information on land management, and where possible, land use history should be systematically recorded for each site. A case study of the agricultural frontier in Brazil is presented in which land use effect factors are calculated in order to quantify the CO2 fluxes from national land use/management conversion matrices. Process-based SOC models can be run for the individual points of the SMN, provided detailed land management records are available. These studies are still rare, as most SMNs have been implemented recently or are in progress. Examples from the USA and Belgium show that uncertainties in SOC change range from 1.6–6.5 Mg C ha−1 for the prediction of SOC stock changes on individual sites to 11.72 Mg C ha−1 or 34% of the median SOC change for soil/land use/climate units. For national SOC monitoring, stratified sampling sites appears to be the most straightforward attribution of SOC values to units with similar soil/land use/climate conditions (i.e. a spatially implicit upscaling approach). Keywords Soil monitoring networks - Soil organic carbon - Modeling - Sampling design