Spatial Random Process Research Articles

Determinants and spatial factors of anemia in women of reproductive age in Democratic Republic of Congo (drc): a Bayesian multilevel ordinal logistic regression model approach

BackgroundAs a global public health problem, anemia affects more than 400 million women of reproductive age worldwide, mostly in Africa and India. In the DRC, the prevalence of anemia has decreased slightly from 52.9% in 2007, to 46.4% in 2012 and 42.4% in 2019. However, there is considerable regional variation in its distribution. The aim of this study is to determine the factors contributing to anemia in women of reproductive age and to explore its spatial distribution in the DRC.MethodsBased on the Bayesian Multilevel Spatial Ordinal Logistic Regression Model, we used the 2013 Democratic Republic of Congo Demographic and Health Survey (DHS-DRC II) data to investigate individual and environmental characteristics contributing to the development of anemia in women of reproductive age and the mapping of anemia in terms of residual spatial effects.ResultsAge, pregnancy status, body mass index, education level, current breastfeeding, current marital status, contraceptive and insecticide-treated net use, source of drinking water supply and toilet/latrine use including the province of residence were the factors contributing to anemia in women of reproductive age in DRC. With Global Moran's I = -0.00279, p-value ≥ 0.05, the spatial distribution of anemia in women of reproductive age in DRC results from random spatial processes. Thus, the observed spatial pattern is completely random.ConclusionThe Bayesian Multilevel Spatial Ordinal Logistic Regression statistical model is able to adjust for risk and spatial factors of anemia in women of reproductive age in DRC highlighting the combined role of individual and environmental factors in the development of anemia in DRC.

Socioeconomic and geospatial determinants of households’ food and non-food consumption dynamics within the West African Economic and Monetary Union

This article explores the cross-sectional properties of household's food and non-food consumption expenditures conceptualized as inter-dependent spatial random processes within the West African Economic and Monetary Union (WAEMU). To this end, the paper applies spatio-temporal econometric methods to data extracted from the first edition of the Harmonized Survey on Household Living Conditions (EHCVM, 2018/2019). The findings from the unconditional distribution of household economic wellbeing (measured by nominal per-capita food and non-food expenditures) using the inequality indicators of the Atkinson and Gini coefficients, suggest the presence of cross-sectional inequalities in household food and non-food wellness within WAEMU. However, food wellness inequality appeared lower than that of non-food wellness across the 8 countries. In addition, the economic security analysis, based on the indices of Watts, Sen, and Foster (aplha=1), highlight important spatial heterogeneity in household's vulnerability to poverty within-and-between WAEMU country members. Moreover, estimation of the semiparametric bivariate Gaussian copula model of food and non-food consumption expenditures, shows their significant dependence with household's demographic and geospatial characteristics, as well as the economic and health characteristics of the household head. Indeed, among other key findings, a gender based gradient in household's food and non-food wellness at respectively 3.6 and 4.4% is observed in favor of male headed households; along with an Urban/Rural divide in food and non-food wellness at 20.7% and 27.3%, respectively, in favor of urban households. Therefore, in line with goals 1, 2, 4, 5, 9 and 10 of the United Nations 2030 Agenda for sustainable development, the paper provides key insights for evidence based policy making within WAEMU.

Modeling SARS-CoV-2 nucleotide mutations as a stochastic process.

This study analyzes the SARS-CoV-2 genome sequence mutations by modeling its nucleotide mutations as a stochastic process in both the time-series and spatial domain of the gene sequence. In the time-series model, a Markov Chain embedded Poisson random process characterizes the mutation rate matrix, while the spatial gene sequence model delineates the distribution of mutation inter-occurrence distances. Our experiment focuses on five key variants of concern that had become a global concern due to their high transmissibility and virulence. The time-series results reveal distinct asymmetries in mutation rate and propensities among different nucleotides and across different strains, with a mean mutation rate of approximately 2 mutations per month. In particular, our spatial gene sequence results reveal some novel biological insights on the characteristic distribution of mutation inter-occurrence distances, which display a notable pattern similar to other natural diseases. Our findings contribute interesting insights to the underlying biological mechanism of SARS-CoV-2 mutations, bringing us one step closer to improving the accuracy of existing mutation prediction models. This research could also potentially pave the way for future work in adopting similar spatial random process models and advanced spatial pattern recognition algorithms in order to characterize mutations on other different kinds of virus families.

PM2.5 Concentrations Variability in North China Explored with a Multi-Scale Spatial Random Effect Model.

Compiling fine-resolution geospatial PM2.5 concentrations data is essential for precisely assessing the health risks of PM2.5 pollution exposure as well as for evaluating environmental policy effectiveness. In most previous studies, global and local spatial heterogeneity of PM2.5 is captured by the inclusion of multi-scale covariate effects, while the modelling of genuine scale-dependent variabilities pertaining to the spatial random process of PM2.5 has not yet been much studied. Consequently, this work proposed a multi-scale spatial random effect model (MSSREM), based a recently developed fixed-rank Kriging method, to capture both the scale-dependent variabilities and the spatial dependence effect simultaneously. Furthermore, a small-scale Monte Carlo simulation experiment was conducted to assess the performance of MSSREM against classic geospatial Kriging models. The key results indicated that when the multiple-scale property of local spatial variabilities were exhibited, the MSSREM had greater ability to recover local- or fine-scale variations hidden in a real spatial process. The methodology was applied to the PM2.5 concentrations modelling in North China, a region with the worst air quality in the country. The MSSREM provided high prediction accuracy, 0.917 R-squared, and 3.777 root mean square error (RMSE). In addition, the spatial correlations in PM2.5 concentrations were properly captured by the model as indicated by a statistically insignificant Moran’s I statistic (a value of 0.136 with p-value > 0.2). Overall, this study offers another spatial statistical model for investigating and predicting PM2.5 concentration, which would be beneficial for precise health risk assessment of PM2.5 pollution exposure.

Electrochemical Evolution of Carbon Steel and Fe-9% Cr Steel Rebar in Simulated Concrete Pore Solution (SCPS) in the Presence of 3.5 wt% NaCl

Carbon steel rebar (ASTM A615) has been widely used in reinforced concrete (RC), but its susceptibility to chloride ions remains a critical issue. Low alloy chromium steel has been used to increase corrosion resistance and extend service life, such as in 9% Cr rebar (ASTM A1035-CS). In this work, we characterized two electrochemical systems over time: ASTM A615 and A1035-CS corrugated rebar immersed in SCPS in the presence of NaCl for 12 months. The interfacial processes evolution for the ASTM A1035-CS rebar for both general and local corrosion showed different active-passive responses from those of carbon steel. Because the 3.5% wt. NaCl exceeded the chloride threshold for passive breakdown of both materials, the ASTM A1035-CS showed a five-fold higher impedance and lower general corrosion rate. In localized conditions, the low alloy chrome content rebar showed less density localized attack than the ASTM A615 rebar. These results were attributed to the overall damage evolution involving the formation and stability of corrosion products over time. The local attack appeared to be a random spatial process due to changes in the local environment.

Partitioning Ground Motion Uncertainty When Conditioned on Station Data

ABSTRACT Rapid estimation of earthquake ground shaking and proper accounting of associated uncertainties in such estimates when conditioned on strong-motion station data or macroseismic intensity observations are crucial for downstream applications such as ground failure and loss estimation. The U.S. Geological Survey ShakeMap system is called upon to fulfill this objective in light of increased near-real-time access to strong-motion records from around the world. Although the station data provide a direct constraint on shaking estimates at specific locations, these data also heavily influence the uncertainty quantification at other locations. This investigation demonstrates methods to partition the within- (phi) and between-event (tau) uncertainty estimates under the observational constraints, especially when between-event uncertainties are heteroscedastic. The procedure allows the end users of ShakeMap to create separate between- and within-event realizations of ground-motion fields for downstream loss modeling applications in a manner that preserves the structure of the underlying random spatial processes.

Geostatistics for Environmental Scientists

There are many theories that are seemly worth linking the environment and statistical methods through a space or space-time sampling framework. A prominent theory of spatial random processes is fully explored in Geostatistics for Environmental Scientists, a book that was first published in 2001, and later revised in a second edition in 2007. The book grasps the definition of ‘Geostatistics’ from a farmer’s imaginary story, to connect it to a soil/environment survey. The soil survey is very important for the authors’ methodology. It is characterized by sampled locations to determine how much is known and how soil/environmental surveys can apply Geostatistics methods to generate estimates and predict values for unknown locations through variogram and covariance.

Generalized least‐squares in dimension expansion method for nonstationary processes

AbstractIn this article, we consider the problem of modeling nonstationary spatial random processes. Bornn et al.(2012) proposed a dimension expansion method, a novel technique for modeling nonstationary processes, aiming to find a dimensionally sparse projection in which the originally nonstationary field exhibits stationarity. However, their dimension expansion approach is a lasso‐penalized least‐squares method that does not account for the covariance structure of the empirical semivariogram. We thus propose a general latent dimension estimation method by replacing the least‐squares method with generalized least‐squares (GLS). Furthermore, we improve the GLS method by weighted least‐squares, which is more computationally efficient and accurate. The performance of the proposed methods is demonstrated through simulations and real data examples.

Scalable Adaptive Batch Sampling in Simulation-Based Design With Heteroscedastic Noise

Abstract In this study, we propose a scalable batch sampling scheme for optimization of simulation models with spatially varying noise. The proposed scheme has two primary advantages: (i) reduced simulation cost by recommending batches of samples at carefully selected spatial locations and (ii) improved scalability by actively considering replicating at previously observed sampling locations. Replication improves the scalability of the proposed sampling scheme as the computational cost of adaptive sampling schemes grow cubicly with the number of unique sampling locations. Our main consideration for the allocation of computational resources is the minimization of the uncertainty in the optimal design. We analytically derive the relationship between the “exploration versus replication decision” and the posterior variance of the spatial random process used to approximate the simulation model’s mean response. Leveraging this reformulation in a novel objective-driven adaptive sampling scheme, we show that we can identify batches of samples that minimize the prediction uncertainty only in the regions of the design space expected to contain the global optimum. Finally, the proposed sampling scheme adopts a modified preposterior analysis that uses a zeroth-order interpolation of the spatially varying simulation noise to identify sampling batches. Through the optimization of three numerical test functions and one engineering problem, we demonstrate (i) the efficacy and of the proposed sampling scheme to deal with a wide array of stochastic functions, (ii) the superior performance of the proposed method on all test functions compared to existing methods, (iii) the empirical validity of using a zeroth-order approximation for the allocation of sampling batches, and (iv) its applicability to molecular dynamics simulations by optimizing the performance of an organic photovoltaic cell as a function of its processing settings.

Space-time simulation of precipitation based on weather pattern sub-sampling and meta-Gaussian model

Simulation methods for design flood estimations in dam safety studies require fine scale precipitation data to provide quality input for hydrological models, especially for extrapolation to extreme events. This leads to use statistical models such as stochastic weather generators. The aim here is to develop a stochastic model adaptable on mountainous catchments in France and accounting for spatial and temporal dependencies in daily precipitation fields. To achieve this goal, the framework of spatial random processes is adopted here.The novelty of the model developed in this study resides in the combination of an autoregressive meta-Gaussian process accounting for the spatio-temporal dependencies and weather pattern sub-sampling discriminating the different rainfall intensity classes. The model is tested from rain gauges in the Ardèche catchment located in South of France. The model estimation is performed in four steps, dealing respectively with: (i) the at-site marginal distribution, (ii) the mapping of the marginal distribution parameters at the target resolution, (iii) the at-site temporal correlation and (iv) the spatial covariance function.The model simulations are evaluated in terms of marginal distribution, inter-site dependence and areal rainfall properties and compared to the observations at calibration stations and also on a set of independent validation stations. Regarding all these aspects, the model shows good abilities to reproduce the observed statistics and presents really small discrepancies compared to the stations data. The sub-sampling is particularly efficient to reproduce the seasonal variations and the marginal mapping procedure induces very small differences in terms of daily rain amounts and daily occurrence probabilities.

Reflection probability in wirelessnetworks with metasurface-coatedenvironmental objects: an approach basedon random spatial processes

Reflection probability in wirelessnetworks with metasurface-coatedenvironmental objects: an approach basedon random spatial processes

An adjusted parameter estimation for spatial regression with spatial confounding

Spatial regression models are often used to analyze the ecological and environmental data sets over a continuous spatial support. Issues of collinearity among covariates have been widely discussed in modeling, but only rarely in discussing the relationship between covariates and unobserved spatial random processes. Past researches have shown that ignoring this relationship (or, spatial confounding) would have significant influences on the estimation of regression parameters. To overcome this problem, an idea of restricted spatial regression is used to ensure that the unobserved spatial random process is orthogonal to covariates, but the related inferences are mainly based on Bayesian frameworks. In this paper, an adjusted generalized least squares estimation method is proposed to estimate regression coefficients, resulting in estimators that perform better than conventional methods. Under the frequentist framework, statistical inferences of the proposed methodology are justified both in theories and via simulation studies. Finally, an application of a water acidity data set in the Blue Ridge region of the eastern U.S. is presented for illustration.

Prediction of spatial functional random processes: comparing functional and spatio-temporal kriging approaches

We present and compare functional and spatio-temporal (Sp.T.) kriging approaches to predict spatial functional random processes (which can also be viewed as Sp.T. random processes). Comparisons with respect to computational time and prediction performance via functional cross-validation is evaluated, mainly through a simulation study but also on a real data set. We restrict comparisons to Sp.T. kriging versus ordinary kriging for functional data (OKFD), since the more flexible functional kriging approaches pointwise functional kriging (PWFK) and the functional kriging total model coincide with OKFD in several situations. Here we formulate conditions under which we show that OKFD and PWFK coincide. From the simulation study, it is concluded that the prediction performance of the two kriging approaches in general is rather equal for stationary Sp.T. processes. However, functional kriging tends to perform better for small sample sizes, while Sp.T. kriging works better for large sizes. For non-stationary Sp.T. processes, with a common deterministic time trend and/or time varying variances and dependence structure, OKFD performs better than Sp.T. kriging irrespective of the sample size. For all simulated cases, the computational time for OKFD was considerably lower compared to those for the Sp.T. kriging methods.

Reflection probability in wireless networks with metasurface-coated environmental objects: an approach based on random spatial processes

An emerging and promising vision of wireless networks consists of coating the environmental objects with reconfigurable metasurfaces that are capable of modifying the radio waves impinging upon them according to the generalized law of reflection. By relying on tools from point processes, stochastic geometry, and random spatial processes, we model the environmental objects with a modified random line process of fixed length and with random orientations and locations. Based on the proposed modeling approach, we develop the first analytical framework that provides one with the probability that a randomly distributed object that is coated with a reconfigurable metasurface acts as a reflector for a given pair of transmitter and receiver. In contrast to the conventional network setup where the environmental objects are not coated with reconfigurable metasurfaces, we prove that the probability that the typical random object acts as a reflector is independent of the length of the object itself. The proposed analytical approach is validated against Monte Carlo simulations, and numerical illustrations are given and discussed.

Improved Spatiotemporal Representativeness and Bias Reduction of Satellite‐Based Evapotranspiration Retrievals via Use of In Situ Meteorology and Constrained Canopy Surface Resistance

AbstractEvapotranspiration (ET) is a key component of the atmospheric and terrestrial water and energy budgets. Satellite‐based vegetation index approaches have used remotely sensed vegetation and reanalysis meteorological properties with surface energy balance models to estimate global ET (MOD16 ET). We reconstructed satellite retrievals using in situ meteorology (Argonne‐ET) and evaluated them using a dense network of surface turbulent heat flux measurements. Argonne‐ET resolves spatial heterogeneity of ET across the U.S. Southern Great Plains that is not well characterized by MOD16; MOD16 ET exhibits spatial autocorrelation (Moran's I significantly >0 in May–Aug.), whereas in situ and Argonne‐ET exhibit characteristics of a random spatial process (Moran's I not significantly different from 0). The skill in resolving ET temporal variability is not significantly different between MOD16 and Argonne‐ET (correlation coefficient = 0.75 and 0.72, respectively). However, the root‐mean‐square errors were significantly lower for Argonne‐ET (36 W/m2) than MOD16 (43 W/m2), and MOD16 exhibits substantial bias in annual ET relative to in situ measurements (−38%). This is attributed to overestimation in the dry canopy surface resistance (rs) parameterization. Using rs constrained to the range of typical measured values, Argonne‐ET substantially reduces the bias in the annual ET (+1%). The improved ET estimates are critical for regional water budget analyses. The methodology presented herein also demonstrates the ability to retrieve high temporally resolved (30 min; cf. 8‐day MOD16) ET that can be used for development of processed‐based diagnostics of model biases and to elucidate avenues to improve ET model parameterizations.

Spatial Prediction for Real Data using Kriging Technique

This study investigates the prediction of unstable random spatial process using the Ordinary Kriging technique, based on the variogram function Y(X,Y) in finding out the predictors, and the universal multivariate technique, which has been applied by computing the Cross Variogram Function. Practically, the data were taken from a geological study conducted in the Department of Geography, Faculty of Education, Mosul University. The study includes the height levels of (40) oil wells in Kirkuk. We discovered out the estimation of the Variogram and Cross the Variogram functions as well as the Mean Squared Error (MSE). Most of the results have been presented in tables and figures and the results were generally good, acceptable and close to reality,Our results showed that the overall Kriging technique or technique that was computed by the Cross Variogram Function was better than the Ordinary Kriging technique or technique based on the variogram function. .

Sufficient Conditions for Reconstructing 2-D Rainfall Maps

The ground level rainfall at a given time is modeled as a 2-D spatial random process ${r}(\textit {x, y})$ , the rain field. Existing measurement equipment, such as rain gauges, weather stations, or recently proposed microwave links, samples ${r}(\textit {x, y})$ spatially in specific points or along lines. Given these samples, our purpose is to reconstruct ${r}(\textit {x, y})$ . In this paper, we study the question: “under what conditions can a given topology of ground measurements guarantee reconstructability of the rain field?” Based on the assumption that rain fields are sparse, we present a statistical approach to this problem by first characterizing the statistics of the measurements, and then answering the question by applying methods from compressed sensing theory, and in particular Donoho and Tanner’s phase transition diagram for sparse recovery. We conclude by suggesting a solution in a form of a simple diagram, allowing one to evaluate the potential reconstruction of ${r}(\textit {x, y})$ in different resolutions without the need for computations.

Investigation of asymmetric spatial dependence of precipitation using empirical bivariate copulas

Precipitation plays an important role in any hydrological analysis. The aim of this study is to empirically investigate the behaviour of spatial dependence of precipitation fields. This would determine whether the Gaussian assumption is fulfilled in regard to symmetric spatial dependence structure between low and high precipitation values. An asymmetry function that can incorporate zero precipitation amounts is introduced on the basis of empirical bivariate copulas. The asymmetry function is calculated by integrating the empirical bivariate copula density in the upper right and the lower left parts for any given quantile thresholds. Zero precipitation amounts are handled as latent variables and the thresholds, therefore, are set to be bigger than probability of zero. The Gaussian simulations based testing is applied for determining the degree of uncertainty. The empirical bivariate copulas are constructed using the concept of regionalized variables in spatial random process with a given separating distance. For any selected time interval, the precipitation over the region of interest is assumed to be a single realization of a spatially stationary random process. The investigations are conducted in Singapore and Bavaria. To take temporal characteristics and seasons into account, precipitation occurrences with different time scales for different seasons are analysed.The empirical evidence proves that the precipitation events tend to follow the positive asymmetric spatial dependence structure, particularly at a short separating distance. This implies that precipitation amounts with higher intensities tends to be more spatially correlated than that with lower intensities because precipitation occurrences tend to occur in a clustered manner. Consequently, spatial precipitation models that are based on the symmetric Gaussian dependence could result in an underestimation of the spatial extent of actual precipitation extremes. Moreover, this pattern is higher for smaller time scales (hourly to daily).

Local linear estimation for spatial random processes with stochastic trend and stationary noise.

We consider the problem of estimating the trend for a spatial random process model expressed as Z(x) = μ(x) + ε(x) + δ(x), where the trend μ is a smooth random function, ε(x) is a mean zero, stationary random process, and {δ(x)} are assumed to be i.i.d. noise with zero mean. We propose a new model for stochastic trend in by generalizing the notion of a structural model for trend in time series. We estimate the stochastic trend nonparametrically using a local linear regression method and derive the asymptotic mean squared error of the trend estimate under the proposed model for trend. Our results show that the asymptotic mean squared error for the stochastic trend is of the same order of magnitude as that of a deterministic trend of comparable complexity. This result suggests from the point of view of estimation under stationary noise, it is immaterial whether the trend is treated as deterministic or stochastic. Moreover, we show that the rate of convergence of the estimator is determined by the degree of decay of the correlation function of the stationary process ε(x) and this rate can be different from the usual rate of convergence found in the literature on nonparametric function estimation. We also propose a data dependent selection procedure for the bandwidth parameter which is based on a generalization of Mallow's C p criterion. We illustrate the methodology by simulation studies and by analyzing a data on surface temperature anomalies.

Seismic Exploration Random Noise on Land: Modeling and Application to Noise Suppression

In seismic exploration, random noise suppression is one of the key problems in seismic data processing. For random noise attenuation, the most important thing is the understanding of seismic random noise generation and propagation. Seismic random noise is considered as temporal and spatial random processes, and it can be analyzed only qualitatively for now, due to its high variability. In this paper, we classify seismic random noise sources by their generation factors and simulate the random noise of the desert in West China. According to Green’s function, it can be assumed that seismic random noise sources are point-like sources that are distributed around geophones. A seismic random noise record is taken as the superimposed wave field exited by all the independent sources in a homogeneous isotropy half-infinite surface. Based on the wind vibration theory and preliminary study about ambient vibrations, the noise source functions are determined. We obtain the waveforms of different kinds of noise by solving the inhomogeneous wave equations and analyze the characteristics qualitatively and quantitatively. The seismic synthetic record with a 1.6-s time and 250-m distances is obtained, and the characteristics are compared between the simulated and the real noise record in time domain and space domain, respectively. The comparative results show the same characteristics of the simulated noise and the real noise, which demonstrates the feasibility of the proposed method. According to the noise modeling, it is known that the near-field cultural noise is the main component of the random noise in the desert, on the basis of which complex diffusion filtering is selected. The filtered results by complex diffusion filtering is compared with the results of time–frequency peak filtering, which is a popular filtering method of seismic random noise suppression in recent years. The comparative results show that complex diffusion filtering is more suitable for the noise of the desert in the Tarim Basin. This result proves that seismic random noise modeling can provide the guidance for noise attenuation. It lays a foundation for researching the propagation characteristics and better attenuation of seismic random noise in the future.