Spatial Correlation Parameters Research Articles

Modelling spatial and temporal correlation in multi-assessment perennial crop variety selection trials using a multivariate autoregressive model

Context Perennial crop variety selection trials are often conducted over several seasons or years. These field trials often exhibit spatial correlation between plots. When data from multiple assessment times are analysed, it is necessary to account for both spatial and temporal correlation. A current approach is to use linear mixed models with separable spatial and temporal residual covariance structures. A limitation of these separable models is that they assume the same spatial correlation structure for each assessment time, which may not hold in practice. Aims This study aims to provide more flexible methods for modelling the spatio-temporal correlation in multi-assessment perennial crop data, allowing for differing spatial parameters for each time, together with modelling genetic effects over time. Methods The paper investigates the suitability of two-directional invariant multivariate autoregressive (2DIMVAR1) models for analysis of multi-assessment perennial crop data. The analysis method is applied to persistence data from a pasture breeding trial. Key results The multivariate autoregressive spatio-temporal residual models are a significant improvement on separable residual models under different genetic models. The paper demonstrates how to fit the models in practice using the software ASReml-R. Conclusions A flexible modelling approach for multi-assessment perennial crop data is presented, allowing differing spatial correlation parameters for each time. The models allow investigation into genotype × time interactions, while optimally accounting for spatial and temporal correlation. Implications The models provide improvements on current approaches and hence will result in more accurate genetic predictions in multi-assessment perennial crop variety selection trials.

Path Learning in Human–Robot Collaboration Tasks Using Iterative Learning Methods

In a repetitive human–robot collaboration (HRC) task, robots typically are required to learn the intended motion of the human user to improve the collaboration efficiency. However, the human user’s trajectory is of uncertainty when repeating the same task (e.g., human hand tremor and uncertain movement speed), which may directly deteriorate the learning performance. To address this issue, a path characterized by spatial correlation parameters, is of necessity to be learned by robots so that the aforementioned time-related uncertainty will be avoided. In this article, based on the path parameterization, a gradient-based iterative path learning (IPL) strategy is designed for the robot to learn the desired path of human. The proposed IPL strategy draws on the iterative learning methods with a properly designed performance index. Since the gradient of the performance index is hard to directly obtain in HRC, two learning methods with gradient search (GS) and gradient estimation (GE) are developed. The GS estimates the gradient online and has an advantage of easy implementation. By contrast, the advantage of GS is more obvious when the number of learned parameters is considerable due to its high learning efficiency. With these two methods, the unknown path parameters can be iteratively updated toward the desired values. To verify the effectiveness of the proposed IPL algorithm, experiments are carried out. In the experiment, a comparison between GS and GE methods is made to display their respective advantages. Besides, the proposed IPL is compared with an existing trajectory learning method subject to two different kinds of uncertainties and its better learning performance verifies its stability and capability in dealing with uncertainty.

Closed‐form expressions for spatial correlation parameters for performance analysis of fluid antenna systems

Closed‐form expressions for spatial correlation parameters for performance analysis of fluid antenna systems

Worst-case effect in bearing capacity of spread foundations considering safety factors and anisotropy in soil spatial variability

ABSTRACT Random field theory is currently the most important tool used when modelling spatial variabilities in soil properties. However, there are practical difficulties in indicating spatial correlation parameters, such as horizontal and vertical fluctuation scales. Therefore, the performed analyses touch upon the occurrence of the worst-case effect of the horizontal fluctuation scale. The random finite element (RFEM) approach is utilised to estimate probability distributions of the bearing capacity of a spread foundation. The analyses show that the observed location of the worst-case phenomenon is closely related to the adopted safety factor. Therefore, it is difficult to directly indicate the horizontal fluctuation scale for which the failure probability has the greatest value. Nevertheless, some general guidelines are formulated and proposed. These general rules can be applied to the two-dimensional bearing capacity problem.

Spatial variability of epi- and mesopelagic 38 kHz backscatter from nekton and macrozooplankton across the southeastern US shelf break

Acoustic echosounders collect detailed information on the location of patchily distributed pelagic organisms over varying spatial scales. This study measured the spatial variability of epi- and mesopelagic 38 kHz backscatter along the US Mid- and South Atlantic continental shelf and slope. We used variogram analysis to estimate the horizontal spatial structure of backscatter measurements, examined whether environmental variables might affect these estimates, and assessed potential impacts of acoustic survey design. Backscatter data were collected during ship-based surveys (50-100 km2) at 7 sites during 4 cruises between November 2017 and November 2019. Average patch size estimates were consistently between 2 and 4 km among locations. Modeled variogram range varied significantly with the depth of the backscatter layer, but linear effect sizes were negligible (<1 m). Chlorophyll a (chl a) concentration had a significant positive effect on range (95 m), suggesting that patch sizes are slightly larger in the epipelagic where chl a concentration is higher. Incorporating variogram parameters of range, sill, and nugget produced some clustering of spatial correlation parameters with scattering layer depth, particularly for the deepest sites assessed (700-900 m depth). Spatial characteristics of a given location were not significantly different between surveys of the same size, but sometimes differed with smaller (25% of area) survey sizes. These results offer insight into nekton and macrozooplankton backscatter patterns in important shelf break and slope systems across horizontal and vertical dimensions, and provide needed information for monitoring fine- to mesoscale offshore marine habitat areas.

Undrained stability analysis of strip footings lying on circular voids with spatially random soil

Random adaptive finite element limit analysis (RAFELA) is introduced to investigate the stability of the footing-voids system with random soils. The emphasis of this study is, for the footing-void system, on quantifying the influence of spatial variability on its bearing capacity and the failure probability. Of particular interest is that random field theory is utilized to characterize the spatial variability of soil, and at the same time, failure probability is calculated by imposing Monte-Carlo simulations on independent cases. Strict close bearing capacity could be obtained within the scope embraced by upper bound (UB) results and lower bound (LB) results. By imposing the proposed modelling, comprehensive parametric studies were carried out, especially for the soil spatial correlation parameters and geometry parameters. The results indicated that the failure probability would increase with the farther distance between the void and the footing, the greater coefficient of variation (COV) and the smaller vertical correlation length. Detailed design tables were presented to assess potential failure probability under different conditions. Typical failure patterns are also summarized, revealing a positive correlation between the failure probability and the diffusion degree of failure curves.

Small area estimation of general parameters: Bayesian transformed spatial prediction approach

For estimating area-specific parameters such as poverty indicators in a finite population, estimators based only on the area-specific samples have typically high variability due to small sample sizes, and model-based methods are recognized to be useful to increase the accuracy of the estimation by borrowing information from related areas. This article proposes an Bayesian approach to this problem based on random effects models. To address the non-normality of response variables and possible spatial correlations among geographically neighboring areas, we introduce random effects models with a parametric family of transformations and spatially correlated random area effects. We assign prior distributions on unknown parameters including transformation and spatial correlation parameters and provide an efficient posterior computation algorithm for estimation and inference for area-specific population parameters via Markov Chain Monte Carlo. We demonstrate the performance of the proposed methods together with existing methods through simulation and empirical studies.

The Impact of Spatial–Temporal Averaging on the Dynamic–Statistical Properties of Rain Fields

Knowledge of the spatial–temporal variation of rain fields is required for the planning and optimization of wide-area high-frequency terrestrial and satellite communication networks. This article presents data and a method for characterizing multi-resolution statistical/dynamic parameters describing the spatial–temporal variation of rain fields across ocean climate in North-Western Europe. The data are derived from the NIMROD network of rain radars. The characterizing parameters include 1) statistical distribution of point 1 min rainfall rates, 2) spatial and temporal correlation functions of rainfall rate, and 3) the probability of rain/no rain. The main contributions of this article are the assessment of the impact of varying spatial and temporal integration lengths on these parameters, their dependencies on the integration volumes and area sizes, and the model for both temporal and spatial correlation parameters.

Effectiveness of spatial analysis in Cryptomeria japonica D. Don (sugi) forward selection revealed by validation using progeny and clonal tests

Accurate evaluation of genetic performances of trees is crucial in order to improve the efficiency of forest tree breeding. We revealed that spatial analysis is effective for predicting individual tree breeding values at the forward selection stage of Cryptomeria japonica D. Don (sugi) breeding program by using a novel validation approach. In the process of selecting genetically superior trees for breeding, appropriate handling of environmental effects is important in order to precisely evaluate candidate trees. Spatial analysis has been an effective statistical approach for genetic evaluation at sites with heterogeneous microenvironments. However, the efficiency of spatial analysis on forward selection has not been validated on a practical scale to date. This study aimed to reveal the effectiveness of spatial analysis, which incorporates spatially autocorrelated residuals into mixed models, for the prediction of breeding values at the forward selection stage by validation using progeny or clonal tests of forward-selected individuals. Tree height was analyzed by ordinary randomized complete block design models and spatial models incorporating spatially autocorrelated residuals in a linear mixed model framework, and model selection was conducted at thirty Cryptomeria japonica D. Don breeding population sites having various topographical ruggedness. For validation, three clonal tests and one progeny test of individuals selected from three and four breeding populations, respectively, were used. The effectiveness of forward selection using the two models was evaluated based on the correlation between individual breeding values at the stage of forward selection and genotypic and breeding values that were estimated by clonal and progeny tests. Spatial models were more predictive than ordinary models in all cases. Spatial correlation parameters tend to increase with the topographical ruggedness index of each site. The correlation coefficients between breeding values at the time of forward selection and genotypic or breeding values evaluated in succeeding clonal and progeny tests were significantly higher in spatial models than in ordinary models in six out of nine cases. Validation using progeny and clonal tests of forward-selected individual trees revealed that spatial analysis is more effective for the evaluation of genetic performance of individuals at the stage of forward selection in Cryptomeria japonica.

Joint Decoding and Estimation of Spatio-Temporally Correlated Binary Sources

In the context of distributed joint source-channel coding, we conceive a joint decoding and estimation scheme for binary Markov sources exhibiting spatio-temporal correlation. The proposed scheme is designed based on the serial concatenation of a trellis coded modulation (TCM) scheme and a unity-rate code. The symbol-based maximum a posteriori algorithm employed for TCM decoding is modified in order to exploit the source correlation. The estimation of both the spatial and temporal correlation parameters is performed jointly with the iterative decoding, hence allowing the estimated parameters to be updated after each iteration. Our simulation results reveal that when both the spatial and temporal correlation parameters are unknown, the proposed joint decoding and estimation scheme approaches the performance to the ideal system relying on perfectly known correlation parameters, therefore, demonstrating the superiority of the proposed scheme.

A stability analysis of a layered-soil slope based on random field

This paper details a method for investigating the stability of a layered slope that combines random field theory with horizontal integration. Both the cohesion and friction coefficient are treated as a Gaussian random field. The closed-form solution of the factor of safety and the probability of failure of the layered slope are derived, in which the effects of spatial correlation lengths and spatial correlation parameters on the stability of the layered slope are considered. The derived probability of failure is greatly affected by the input spatial correlation length of the soil parameters. The effectiveness of this proposed method is validated with the results of the Monte Carlo simulation.

Analysis of Spatial Data with a Nested Correlation Structure

SummarySpatial statistical analyses are often used to study the link between environmental factors and the incidence of diseases. In modelling spatial data, the existence of spatial correlation between observations must be considered. However, in many situations, the exact form of the spatial correlation is unknown. This paper studies environmental factors that might influence the incidence of malaria in Afghanistan. We assume that spatial correlation may be induced by multiple latent sources. Our method is based on a generalized estimating equation of the marginal mean of disease incidence, as a function of the geographical factors and the spatial correlation. Instead of using one set of generalized estimating equations, we embed a series of generalized estimating equations, each reflecting a particular source of spatial correlation, into a larger system of estimating equations. To estimate the spatial correlation parameters, we set up a supplementary set of estimating equations based on the correlation structures that are induced from the various sources. Simultaneous estimation of the mean and correlation parameters is performed by alternating between the two systems of equations.

Experimental determination of the correlation properties of plasma turbulence using 2D BES systems

A procedure is presented to map from the spatial correlation parameters of a turbulent density field (the radial and binormal correlation lengths and wavenumbers, and the fluctuation amplitude) to correlation parameters that would be measured by a beam emission spectroscopy (BES) diagnostic. The inverse mapping is also derived, which results in resolution criteria for recovering correct correlation parameters, depending on the spatial response of the instrument quantified in terms of point-spread functions (PSFs). Thus, a procedure is presented that allows for a systematic comparison between theoretical predictions and experimental observations. This procedure is illustrated using the Mega-Ampere Spherical Tokamak BES system and the validity of the underlying assumptions is tested on fluctuating density fields generated by direct numerical simulations using the gyrokinetic code GS2. The measurement of the correlation time, by means of the cross-correlation time-delay method, is also investigated and is shown to be sensitive to the fluctuating radial component of velocity, as well as to small variations in the spatial properties of the PSFs.

Residual Variance–Covariance Modelling in Analysis of Multivariate Data from Variety Selection Trials

Field trials for variety selection often exhibit spatial correlation between plots. When multivariate data are analysed from these field trials, there is the added complication in having to simultaneously account for correlation between the traits at both the residual and genetic levels. This may be temporal correlation in the case of multi-harvest data from perennial crop field trials, or between-trait correlation in multi-trait data sets. Use of parsimonious yet plausible models for the variance–covariance structure of the residuals for such data is a key element to achieving an efficient and inferentially sound analysis. In this paper, a model is developed for the residual variance–covariance structure firstly by considering a multivariate autoregressive model in one spatial direction and then extending this to two spatial directions. Conditions for ensuring that the processes are directionally invariant are presented. Using a canonical decomposition, these directionally invariant processes can be transformed into a set of independent separable processes. This simplifies the estimation process. The new model allows for flexible modelling of the spatial and multivariate interaction and allows for different spatial correlation parameters for each harvest or trait. The methods are illustrated using data from lucerne breeding trials at several environments.

Comparison of spatial correlation parameters between full and model scale launch vehicles

The current vibro-acoustic analysis tools require specific spatial correlation parameters as input to define the liftoff acoustic environment experienced by the launch vehicle. Until recently, these parameters have not been very well defined. A comprehensive set of spatial correlation data were obtained during a scale model acoustic test conducted in 2014. From these spatial correlation data, several parameters were calculated: the decay coefficient, the diffuse to propagating ratio, and the angle of incidence. Spatial correlation data were also collected on the EFT-1 flight of the Delta IV vehicle which launched on December 5, 2014. A comparison of the spatial correlation parameters from full scale and model scale data will be presented.

A spatially autoregressive and heteroskedastic space-time pedestrian exposure modeling framework with spatial lags and endogenous network topologies

The main objective of this study is to derive a modeling framework for characterizing the space-time exposure of pedestrians in crosswalks, where the spatial measure is characterized by pedestrian density and the temporal measure is characterized by crosswalk time occupancy. This characterization has not been observed in the literature, but is a characterization that allows one to differentiate the components of pedestrian exposure with enhanced resolution in space and time. However, real-time observations to generate space-time data are time consuming and expensive over a large urban network. A hybrid microsimulation-statistical approach is utilized for data generation and statistical analysis in this study. The exposure models predicting crosswalk density and occupancy were estimated using spatial autoregressive models with spatial lags, autoregressive and heteroskedastic spatial disturbances and endogenous regressors. An instrumental variables generalized method of moments (IV-GMM) approach was used for estimation, and the spatial models account for spatial dependence among crosswalks through the estimation of spatial lag and spatial correlation parameters. In a case study of the downtown crosswalk grid in Seattle, Washington, 688 crosswalks were modeled using ten network topology measures capturing node degree, centrality, clustering, modularity, attractiveness and eccentricity measures. The models utilized these network topology variables to account for stochasticity in network design effects on pedestrian dynamics. Several important findings resulted from this study. First, and most important, it was found that network topology measures had an endogenous impact on pedestrian density. Second, the pedestrian time occupancy equation is characterized by endogenous selection effects. That is, in crosswalks with persistent pedestrian volumes and positive densities, the impact of pedestrian trip generation volumes and pedestrian density were corrected for endogeneity and selection bias. The combined results of the pedestrian density and time occupancy equations indicate that endogeneity and selection bias are critical issues that should not be ignored in pedestrian exposure modeling. Pedestrian trip generation volumes representing block level facility generation were found to be elastic. This finding indicates the utility of our modeling framework for estimating the impact of land use on pedestrian space-time exposure at the block level. Out-of-sample prediction tests of the density and time occupancy models and comparisons with pedestrian count data from field observations indicated substantial predictive accuracies. Finally, it was determined that degree and hub were highly sensitive network design parameters in terms of their influence on density. The average total impact (marginal effect) of these measures indicates that attention should be paid to crosswalk network design from the standpoint of degree and hub characteristics. These results show that our space-time density-occupancy modeling framework is a plausible and efficient predictive tool that can be used to estimate pedestrian crosswalk exposure using building level and network topology data alone. We find that the IV-GMM technique is a useful approach for the emergent problem of inference in hybrid simulation-statistical transportation datasets, due to fewer assumptions on distributional assumptions about the data, while accounting for statistical effects relating to endogeneity, potential selection effects and heteroscedasticity.

Power of Moran’s I Test for Spatial Dependence in Panel Data Models with Time Varying Spatial Weights Matrices

AbstractThe spatial weights matrix is usually specified to be time invariant. However, when it are constructed with economic/socioeconomic distance, trade /demographic/climatic characteristics, these characteristics might be changing over time, and then the spatial weights matrix substantially varies over time. This paper focuses on power of Moran’s I test for spatial dependence in panel data models with where spatial weights matrices can be time varying (TV-Moran). Compared with Moran’s I test with time invariant spatial weights matrices (TI-Moran), the empirical power of TV-Moran test for spatial dependence are evaluated. Our extensive Monte Carlo simulation results indicate that Moran’s I test with misspecified time invariant spatial weights matrices is questionable; Instead, TV-Moran test has shown superiority in higher power, especially for cases with negative spatial correlation parameters and the large time dimension.

Efficient estimation and prediction for the Bayesian binary spatial model with flexible link functions.

Spatial generalized linear mixed models (SGLMMs) are popular models for spatial data with a non-Gaussian response. Binomial SGLMMs with logit or probit link functions are often used to model spatially dependent binomial random variables. It is known that for independent binomial data, the robit regression model provides a more robust (against extreme observations) alternative to the more popular logistic and probit models. In this article, we introduce a Bayesian spatial robit model for spatially dependent binomial data. Since constructing a meaningful prior on the link function parameter as well as the spatial correlation parameters in SGLMMs is difficult, we propose an empirical Bayes (EB) approach for the estimation of these parameters as well as for the prediction of the random effects. The EB methodology is implemented by efficient importance sampling methods based on Markov chain Monte Carlo (MCMC) algorithms. Our simulation study shows that the robit model is robust against model misspecification, and our EB method results in estimates with less bias than full Bayesian (FB) analysis. The methodology is applied to a Celastrus Orbiculatus data, and a Rhizoctonia root data. For the former, which is known to contain outlying observations, the robit model is shown to do better for predicting the spatial distribution of an invasive species. For the latter, our approach is doing as well as the classical models for predicting the disease severity for a root disease, as the probit link is shown to be appropriate. Though this article is written for Binomial SGLMMs for brevity, the EB methodology is more general and can be applied to other types of SGLMMs. In the accompanying R package geoBayes, implementations for other SGLMMs such as Poisson and Gamma SGLMMs are provided.

A practical two‐step approach for mixed model‐based kriging, with an application to the prediction of soil organic carbon concentration

SummarySoil scientists often use prediction models to obtain values at unsampled locations. The spatial variation in the soil is best captured by using the empirical best linear unbiased predictor (EBLUP) based on a restricted maximum likelihood (REML) approach that efficiently exploits available data on both mean trends and correlation structures. We proposed a practical two‐step implementation of the REML approach for model‐based kriging, exemplified by predicting soil organic carbon (SOC) concentrations in mineral soils in Estonia from the large‐scale digital soil map information and a previously established prediction model. The prediction model was a linear mixed model with soil type, physical clay content (particle size < 0.01 mm) and A‐horizon thickness as fixed effects and site, transect, plot, year, year‐transect random intercepts and site‐specific random slopes for clay content. We used only the site‐specific intercept EBLUPs for estimating spatial correlation parameters as they described most of the variation in the random effects (86.8%). Fitting an exponential correlation model to these EBLUPs resulted in an estimated range of 10.5 km and the estimated proportion of the variance from the nugget effect was 0.23. The results of a simulation study showed a downwards bias that decreased with sample size. The results were validated through an external dataset, resulting in root mean square errors (RMSE) of 1.06 and 1.07% for the two‐step approach for kriging and the model with only fixed effects (no kriging), respectively. These results indicate that using the two‐step approach for kriging may improve prediction.

Impact of soil heterogeneity on the functioning of horizontal ground heat exchangers

The impact of heterogeneity in soil thermal properties on the performance of horizontal ground heat exchangers (HGHE) is closely examined using a custom-made finite element model. Ensembles of heterogeneous soil fields were generated with spatial correlation parameters derived from similar studies of heterogeneity in hydraulic parameters. Within these soil fields, a single loop HGHE was modelled as discrete pipes placed in a heterogeneous soil continuum. The effect of heterogeneity was found to be minimal relative to uncertainty of the mean soil thermal conductivity, supporting the continued use of the assumption of homogeneity when modelling and designing these systems. Multiple design techniques were identified which would allow HGHE designers to further mitigate any deleterious effects, such as preferential heat transfer between adjacent pipes which may act as a ‘short-circuit’ mechanism, reducing HGHE effectiveness.