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1.
Estimating temporal change in soil monitoring: I. Statistical theory   总被引：1，自引：0，他引：1  
Detecting small temporal change of spatially varying soil properties demands precise estimation. Design– and model–based methods are compared for estimating temporal change of soil properties over finite areas. Analytical expressions for the estimators and their variances arc derived for the two approaches, and formulae for the expectations of the variances under the random–process model are developed. Among the randomized designs simple, stratified, and systematic random sampling using the arithmetic mean as estimator have been studied. Pairing the sampling positions on the different occasions increases the precision of design–based estimation if the observations are positively cross–correlated. The relative precisions of the means of stratified and systematic samples depends on the spatial correlation. Neither is more precise than the other in all circumstances. The stratified design provides an unbiased estimator for the sampling error, which is not available from systematic samples. Theoretically, the geostatistical global estimator is more precise than the estimates derived from any of the classical designs when many realizations arc repeatedly sampled at random. In practice, with only a single realization of the process, this is no longer relevant. Moreover, errors in estimating the variograms add to the total error of the method. It seems that only by sampling from large auto–correlated random fields can the precisions of the methods be compared in practice.  相似文献   

2.
Spatially nested sampling and the associated nested analysis of variance by spatial scale is a well-established methodology for the exploratory investigation of soil variation over multiple, disparate scales. The variance components that can be estimated this way can be accumulated to approximate the variogram. This allows us to identify the important scales of variation, and the general form of the spatial dependence, in order to plan more detailed sampling by design-based or model-based methods. Implicit in the standard analyses of nested sample data is the assumption of homogeneity in the variance, i.e. that all variations from sub-station means at some scale represent a random variable of uniform variance. If this assumption fails then the comparable assumption of stationarity in the variance, which is an important assumption in geostatistics, will also be implausible. However, data from nested sampling may be analysed with a linear mixed model in which the variance components are parameters which can be estimated by residual maximum likelihood (REML). Within this framework it is possible to propose an alternative variance parameterization in which the variance depends on some auxiliary variable, and so is not generally homogeneous. In this paper we demonstrate this approach, using data from nested sampling of chemical and biogeochemical soil properties across a region in central England, and use land use as our auxiliary variable to model non-homogeneous variance components. We show how the REML analysis allows us to make inferences about the need for a non-homogeneous model. Variances of soil pH and cation exchange capacity at different scales differ between these land uses, but a homogeneous variance model is preferable to such non-homogeneous models for the variance of soil urease activity at standard concentrations of urea.  相似文献   

3.
Variance componentsare quantities of central interest in many applications, e.g., in cultivar yield stability analysis and in the analysis of measurement errors. In some applications, the feasible sample size is rather limited, leading to estimates of variance components that are subject to considerable sampling variation. For example, new crop cultivars are tested in only a few environments before release to the market, so the sample size for the variance across environments is small. Similarly, testing a new measurement instrument for some chemical compound may be costly, allowing only a limited number of replications. This article investigates the potential for improving the usual sample variance estimator by exploiting covariate information. In a cultivartrial, yield data may be available for only a few environments while meteorological data or data on a standard cultivar has been recorded for a very large number of environments. Likewise, in the analysis of measurement errors, there may be long-term data on a standard measurement procedure that can be used as a covariate to improve the variance estimate for a new instrument. It is shown in this article that the gain in accuracy achieved by using a covariate can be considerable, provided there is sufficient correlation between the covariate and the variable of interest.  相似文献   

4.
Designing an efficient sampling scheme for a rare and clustered population is a challenging area of research. Adaptive cluster sampling, which has been shown to be viable for such a population, is based on sampling a neighborhood of units around a unit that meets a specified condition. However, the edge units produced by sampling neighborhoods have proven to limit the efficiency and applicability of adaptive cluster sampling. We propose a sampling design that is adaptive in the sense that the final sample depends on observed values, but it avoids the use of neighborhoods and the sampling of edge units. Unbiased estimators of population total and its variance are derived using Murthy’s estimator. The modified two-stage sampling design is easy to implement and can be applied to a wider range of populations than adaptive cluster sampling. We evaluate the proposed sampling design by simulating sampling of two real biological populations and an artificial population for which the variable of interest took the value either 0 or 1 (e.g., indicating presence and absence of a rare event). We show that the proposed sampling design is more efficient than conventional sampling in nearly all cases. The approach used to derive estimators (Murthy’s estimator) opens the door for unbiased estimators to be found for similar sequential sampling designs.  相似文献   

5.
Four different parameter-rich process-based models of forest biogeochemistry were analysed in a Bayesian framework consisting of three operations: (1) Model calibration, (2) Model comparison, (3) Analysis of model-data mismatch.Data were available for four output variables common to the models: soil water content and emissions of N2O, NO and CO2. All datasets consisted of time series of daily measurements. Monthly averages and quantiles of the annual frequency distributions of daily emission rates were calculated for comparison with equivalent model outputs. This use of the data at model-appropriate temporal scale, together with the choice of heavy-tailed likelihood functions that accounted for data uncertainty through random and systematic errors, helped prevent asymptotic collapse of the parameter distributions in the calibration.Model behaviour and how it was affected by calibration was analysed by quantifying the normalised RMSE and r2 for the different output variables, and by decomposition of the MSE into contributions from bias, phase shift and variance error. The simplest model, BASFOR, seemed to underestimate the temporal variance of nitrogenous emissions even after calibration. The model of intermediate complexity, DAYCENT, simulated the time series well but with large phase shift. COUP and MoBiLE-DNDC were able to remove most bias through calibration.The Bayesian framework was shown to be effective in improving the parameterisation of the models, quantifying the uncertainties in parameters and outputs, and evaluating the different models. The analysis showed that there remain patterns in the data - in particular infrequent events of very high nitrogenous emission rate - that are unexplained by any of the selected forest models and that this is unlikely to be due to incorrect model parameterisation.  相似文献   

6.
《Geoderma》2005,124(3-4):293-317
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7.
Abundance and standard error estimates in surveys of fishery resources typically employ classical design-based approaches, ignoring the influences of non-design factors such as varying catchability. We developed a Bayesian approach for estimating abundance and associated errors in a fishery survey by incorporating sampling and non-sampling variabilities. First, a zero-inflated spatial model was used to quantify variance components due to non-sampling factors; second, the model was used to calibrate the estimated abundance index and its variance using pseudo empirical likelihood. The approach was applied to a winter dredge survey conducted to estimate the abundance of blue crabs (Callinectes sapidus) in the Chesapeake Bay. We explored the properties of the calibration estimators through a limited simulation study. The variance estimator calibrated on posterior sample performed well, and the mean estimator had comparable performance to design-based approach with slightly higher bias and lower (about 15% reduction) mean squared error. The results suggest that application of this approach can improve estimation of abundance indices using data from design-based fishery surveys.  相似文献   

8.
One of the most important needs for wildlife managers is an accurate estimate of population size. Yet, for many species, including most marine species and large mammals, accurate and precise estimation of numbers is one of the most difficult of all research challenges. Open-population capture-recapture models have proven useful in many situations to estimate survival probabilities but typically have not been used to estimate population size. We show that open-population models can be used to estimate population size by developing a Horvitz-Thompson-type estimate of population size and an estimator of its variance. Our population size estimate keys on the probability of capture at each trap occasion and therefore is quite general and can be made a function of external covariates measured during the study. Here we define the estimator and investigate its bias, variance, and variance estimator via computer simulation. Computer simulations make extensive use of real data taken from a study of polar bears (Ursus maritimus) in the Beaufort Sea. The population size estimator is shown to be useful because it was negligibly biased in all situations studied. The variance estimator is shown to be useful in all situations, but caution is warranted in cases of extreme capture heterogeneity.  相似文献   

9.
Generalized additive models (GAMs) have become popular in the air pollution epidemiology literature. Two problems, recently surfaced, concern implementation of these semiparametric models. The first problem, easily corrected, was laxity of the default convergence criteria. The other, noted independently by Klein, Flanders, and Tolbert, and Ramsay, Burnett, and Krewski concerned variance estimates produced by commercially available software. In simulations, they were as much as 50% too small. We derive an expression for a variance estimator for the parametric component of generalized additive models that can include up to three smoothing splines, and show how the standard error (SE) estimated by this method differs from the corresponding SE estimated with error in a study of air pollution and emergency room admissions for cardiorespiratory disease. The derivation is based on asymptotic linearity. Using Monte Carlo experiments, we evaluated performance of the estimator in finite samples. The estimator performed well in Monte Carlo experiments, in the situations considered. However, more work is needed to address performance in additional situations. Using data from our study of air pollution and cardiovascular disease, the standard error estimated using the new method was about 10% to 20% larger than the biased, commercially available standard error estimate.  相似文献   

10.
When generating experimental designs for field trials laid out on a rectangular grid of plots, it is useful to allow for blocking in both rows and columns. When the design is nonresolvable, randomized classical row–column designs may occasionally involve clustered placement of several replications of a treatment. In our experience, this feature prevents the more frequent use of these useful designs in practice. Practitioners often prefer a more even distribution of treatment replications. In this paper we illustrate how spatial variance–covariance structures can be used to achieve a more even distribution of treatment replications across the field and how such designs compare with classical row–column designs in terms of efficiency factors. We consider both equally and unequally replicated designs, including partially replicated designs. Supplementary materials accompanying this paper appear online.  相似文献   

11.
The need for aquatic resource condition surveys at scales that are too extensive to census has increased in recent years. Statistically designed sample surveys are intended to meet this need. Simple or stratified random sampling or systematic survey designs are often used to obtain a representative set of sites for data collection. However, such designs have limitations when applied to spatially distributed natural resources, like stream networks. Stevens and Olsen proposed a design that overcomes the key limitations of simple, stratified random or systematic designs by selecting a spatially balanced sample. The outcome of a spatially balanced sample is an ordered list of sampling locations with spatial distribution that balances the advantages of simple or stratified random samples or systematic samples. This approach can be used to select a sample of sites for particular studies to meet specific objectives. This approach can also be used to select a “master sample” from which subsamples can be drawn for particular needs. At the same time, these individual samples can be incorporated into a broader design that facilitates integrated monitoring and data sharing.  相似文献   

12.
Agricultural experiments are often laid out in a rectangle in 3?C5 replicates. Is it better to use a standard randomized complete-block design in rows, or a complete-block design in rows but with restricted randomization, or an efficient row-column design? These approaches differ in the variance of the estimator of a difference between two treatments, and in the bias of the estimator of that variance, as well as in the mechanics of constructing the design and analyzing the data. I conclude that when intra-column correlations are high then the row-column design is best but that when they are moderate the best procedure is to use an improved version of restricted randomization, which gives an unbiased estimator of the average variance in the single experiment performed.  相似文献   

13.
Soil pH, hydrolytic acidity (HA), organic matter (OM) and plant available phosphorus (AP) are factors controlling the environmental-friendly soil management in agroecosystems. These parameters are highly variable in space. The objective of this work is to study spatial variability of pH, HA, OM and AP using several interpolation methods in Eastern Croatia. A total of 1004 (0–30 cm) soil samples were collected, and several univariate and multivariate interpolation performances were tested. The results showed that soils of the study area had high HA and AP, while pH and OM were low. The variogram analysis revealed different spatial structures among studied soil properties and demonstrate a need for variable-rate management. Soil pH and OM had lower spatial variability compared to AP and HA. Ordinary kriging was the most accurate method to estimate the studied variables. The incorporation of auxiliary variables increased the precision of the estimations for HA. Soil AP and OM showed different results for spatial prediction obtained by co-kriging. Overall, the incorporation of pH as auxiliary variable increased the prediction of the models. However, more co-variates should be incorporated in further models, in order to identify with more precision areas that need to be restored.  相似文献   

14.
Hourly pedometer counts and irregularly measured concentration of the hormone progesterone were available for a large number of dairy cattle. A hidden semi-Markov was applied to this bivariate time-series data for the purposes of monitoring the reproductive status of cattle. In particular, the ability to identify oestrus is investigated as this is of great importance to farm management. Progesterone concentration is a more accurate but more expensive method than pedometer counts, and we evaluate the added benefits of a model that includes this variable. The resulting model is biologically sensible, but validation is difficult. We utilize some auxiliary data to demonstrate the model’s performance.  相似文献   

15.
The precision of design‐based sampling strategies can be increased by using regression models at the estimation stage. A general regression estimator is given that can be used for a wide variety of models and any well‐defined sampling design. It equals the π estimator plus an adjustment term that accounts for the differences between the π estimators for the spatial means of the auxiliary variables and the true spatial means of these variables. The regression estimator and ratio estimator follow from certain assumptions on the model and the sampling design. These are compared with the π estimator in two case studies. In one study a bivariate field of linearly related variables was simulated and repeatedly sampled by Simple Random Sampling without replacement and sample sizes 10, 25, 50, 100 and 200. For all sample sizes the ratio of the standard error of the simple regression estimator to that of the π estimator was approximately 55%. The bias of the simple regression estimator was negligibly small. The confidence interval estimators were valid for all sample sizes except for n = 10. Also the ratio estimator was approximately unbiased, and the confidence interval estimators were valid for all sample sizes, even for n = 10. This is remarkable because the ratio estimator assumes that the intercept of the regression line is 0 which was incorrect for the simulated field. On the other hand, only approximately 55% of the potential gain was achieved because the model was inappropriate. In a second study the spatial means of the Mean Highest Watertable of map units were estimated by Stratified Simple Random Sampling and the combined (multiple) regression estimator. The NAP elevation, the local elevation, the Easting and the Northing were used as auxiliary variables. For all map units except one the combined (multiple) regression estimator was more precise than the π estimator. The ratio of the standard errors varied from 0.36 to 1.04. The domain for which the regression estimator was less precise than the π estimator showed strong variation between strata. For this domain it was more efficient to group the strata into two groups and to fit simple models for these groups separately.  相似文献   

16.
Spatial design and analysis are widely used, particularly in field experimentation. However, it is often the case that spatial analysis does not significantly enhance more traditional approaches such as row–column analysis. It is then of interest to gauge the degree of error variance bias that accrues when a spatially designed experiment is analysed as a row–column design. This paper uses uniformity data to study error variance bias in \(7\times 12\) spatial designs for 21 treatments.  相似文献   

17.
《Geoderma》2002,105(3-4):259-275
Neglecting the spatial variation in soil nutrient status may result in unused yield potential and in environmental damage. Site-specific management has been suggested to reduce inappropriate fertilization that can adversely affect soil, ground and surface water. Decision criteria for determining variable-rate nitrogen fertilization are, however, lacking. This paper analyses the spatial variation of nitrate nitrogen (NO3–N) and soil properties related to the N cycle at the plot-scale. Three 50×50 m plots were sampled in nested sampling designs of varying complexities. Classical statistics revealed a characteristic ranking in the variability of soil properties. Geostatistical analysis of the NO3–N data from two plots showed that the small-scale variation found in one small subgrid was not typical for the small-scale variation in the entire plot, indicating bias in the sampling design. A trend component was found in the NO3–N data and, consequently, the minimal requirement for the regionalized variable theory was not fulfilled. Problems due to design were overcome with a more complex nested sampling at the third plot. However, the spherical model fitted to the NO3–N data of the first year explained only 21% of the total variance, whereas a pure nugget effect was observed in the second year. The water content data also showed a low structural variance, which was different in the two years. In contrast, two thirds of the variance of total carbon (Ct) and total nitrogen (Nt) could be explained by the fitted models. Seasonal variations, such as varying duration of snow cover, and extrinsic management effects, such as growing of a cover crop, may have contributed to the observed differences in variability between the years. Due to the low proportion of structural variance and the observation that spatial distribution was not stable with time, geostatistical analysis of NO3–N and water contents data added only little information to classical statistical analysis. However, geostatistical analysis of total C and N contents provided a useful means to calculate spatial distribution patterns of these properties.  相似文献   

18.
This paper introduces a new sampling design in a finite population setting, where potential sampling units have a wealth of auxiliary information that can be used to rank them into partially ordered sets. The proposed sampling design selects a set of sampling units. These units are judgment ranked without measurement by using available auxiliary information. The ranking process allows ties among ranks whenever units cannot be ranked accurately with high confidence. The ranking information from all sources is combined in a meaningful way to construct strength-of-agreement weights. These weights are then used to select a single sampling unit for full measurement in each set. Three different levels of sampling design, level-0, level-1, and level-2, are investigated. They differ in their replacement policies. Level-0 sampling designs construct the sample by sampling with replacement, level-1 sampling designs constructs the sample without replacement of the fully measured unit in each set, and level-2 sampling designs construct the sample without replacement on the entire set. For these three designs, we estimate the first and second order inclusion probabilities and construct estimators for the population total and mean. We develop a bootstrap resampling procedure to estimate the variances of the estimators and to construct percentile confidence intervals for the population mean and total. We show that the new sampling designs provide a substantial amount of efficiency gain over their competitor designs in the literature.  相似文献   

19.
《Soil & Tillage Research》1988,12(3):235-251
Short-term temporal changes in bulk density and related soil-water properties of a tilled soil may appreciably influence the processes of infiltration, soil water storage, runoff and erosion. Using a properly-calibrated surface gamma-neutron gauge, the changes in bulk density and moisture content within the topsoil layer can be measured in situ and at a large number of locations, with a minimum amount of time and expense. In this study on a Bernow loam soil (Typic Paleudult), factory calibration for either the neutron or the gamma component of a Troxler gauge was found unsatisfactory when compared with soil cores. Field calibration was obtained for both these components. Two different methods tried for gamma calibration gave satisfactory and nearly the same results. These findings generally agreed with the results for two other soils, whose data were available from an earlier study. Using field calibrations, soil bulk density was measured weekly at several sites within 4 freshly-tilled plots, one left bare, two planted to corn and one to soya bean, in depth intervals of 0–10, 10–20 and 20–30 cm. The plots were irrigated 3 days before each measurement. Over a 15-week period, the major changes in bulk density occurred only within the 0–10-cm layer, and these changes were strongly correlated with the amount of water applied. The presence of crops did not significantly influence these changes measured in the interrow areas. However, some additional data in the 0–10-cm layer indicated that roots may modify soil bulk density in the crop row and interrow areas differently. Measurements of this type serve to provide important information for improving soil and water management.  相似文献   

20.
This paper compares three models that use soil type information from point observations and a soil map to map the topsoil organic matter content for the province of Drenthe in the Netherlands. The models differ in how the information on soil type is obtained: model 1 uses soil type as depicted on the soil map for calibration and prediction; model 2 uses soil type as observed in the field for calibration and soil type as depicted on the map for prediction; and model 3 uses observed soil type for calibration and a pedometric soil map with quantified uncertainty for prediction. Calibration of the trend on observed soil type resulted in a much stronger predictive relationship between soil organic matter content and soil type than calibration on mapped soil type. Validation with an independent probability sample showed that model 3 out‐performed models 1 and 2 in terms of the mean squared error. However, model 3 over‐estimated the prediction error variance and so was too pessimistic about prediction accuracy. Model 2 performed the worst: it had the largest mean squared error and the prediction error variance was strongly under‐estimated. Thus validation confirmed that calibration on observed soil type is only valid when the uncertainty about soil type at prediction sites is explicitly accounted for by the model. We conclude that whenever information about the uncertainty of the soil map is available and both soil property and soil type are observed at sampling sites, model 3 can be an improvement over the conventional model 1.  相似文献   

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