The variability of rainfall acidity

Two years of rainfall acidity data for the eastern United States were analyzed. The data consist of rainfall-event pH measurements from a nine station monitoring network. A spatio-temporal stochastic model, including deterministic components for seasonal variation and rainfall washout, and stochastic components for spatial, temporal, and measurement variation, was fitted to the data. The fitted autocorrelation structure from this model was used, in the process known as Kriging, to obtain BLUE contour maps of seasonal and rainfall adjusted yearly average pH over the monitoring region.     

Approximate Bayesian Inference in Spatial Generalized Linear Mixed Models

Abstract.  In this paper we propose fast approximate methods for computing posterior marginals in spatial generalized linear mixed models. We consider the common geostatistical case with a high dimensional latent spatial variable and observations at known registration sites. The methods of inference are deterministic, using no simulation-based inference. The first proposed approximation is fast to compute and is 'practically sufficient', meaning that results do not show any bias or dispersion effects that might affect decision making. Our second approximation, an improvement of the first version, is 'practically exact', meaning that one would have to run MCMC simulations for very much longer than is typically done to detect any indication of error in the approximate results. For small-count data the approximations are slightly worse, but still very accurate. Our methods are limited to likelihood functions that give unimodal full conditionals for the latent variable. The methods help to expand the future scope of non-Gaussian geostatistical models as illustrated by applications of model choice, outlier detection and sampling design. The approximations take seconds or minutes of CPU time, in sharp contrast to overnight MCMC runs for solving such problems.     

塔河缝洞型油藏溶洞相多点统计学建模方法

塔河油田奥陶系缝洞型碳酸盐岩储集空间多样，非均质性极强，其储集体发育并非受控于沉积相，而是受控于构造岩溶作用，因此常规储层建模思路和方法很难适用。在缝洞单元研究的基础上提出了岩溶相的概念，进行了单井岩溶相划分，通过训练图像建立了溶洞相模式，采用多点统计学方法模拟了溶洞相分布，以岩相分布模型作为约束，利用序贯算法实现了溶洞相孔隙定量建模，为此类油藏的储层建模和剩余油研究提供了有效手段。     

Conditioning of Marked Point Processes within a Bayesian Framework

Shale units with low permeability create barriers to fluid flow in a sandstone reservoir. A spatial stochastic model for the location of shale units in a reservoir is defined. The model is based on a marked point process formulation, where the marks are parameterized by random functions for the shape of a shale unit. This extends the traditional formulation in the sense that conditioning on the actual observations of the shale units is allowed in an arbitrary number of wells penetrating the reservoir. The marked point process for the shale units includes spatial interaction of units and allows a random number of units to be present. The model is defined in a Bayesian setting with prior pdfs assigned to size–shape parameters of shale units. The observations of shales in wells are associated with a likelihood function. The posterior pdf of the marked point process can only partially be developed analytically; the final solution must be determined by sampling using the Metropolis–Hastings algorithm. An example is presented, demonstrating the consequences of increasing the number of wells in which observations are made.     

Estimating the probability of simultaneous rainfall extremes within a region: a spatial approach

In this paper we investigate the impact of model mis-specification, in terms of the dependence structure in the extremes of a spatial process, on the estimation of key quantities that are of interest to hydrologists and engineers. For example, it is often the case that severe flooding occurs as a result of the observation of rainfall extremes at several locations in a region simultaneously. Thus, practitioners might be interested in estimates of the joint exceedance probability of some high levels across these locations. It is likely that there will be spatial dependence present between the extremes, and this should be properly accounted for when estimating such probabilities. We compare the use of standard models from the geostatistics literature with max-stables models from extreme value theory. We find that, in some situations, using an incorrect spatial model for our extremes results in a significant under-estimation of these probabilities which – in flood defence terms – could lead to substantial under-protection.     

Comparisons of changepoint estimators

Statistical comparisons of several nonparametric changepoint estimators which are currently offered in the literature are undertaken. The criteria for comparison are Pitman nearness, probability concentration and mean squared error. Recommendations for small, moderate and large sample cases are given.     

Application of Geostatistics to Risk Assessment

Geostatistics offers two fundamental contributions to environmental contaminant exposure assessment: (1) a group of methods to quantitatively describe the spatial distribution of a pollutant and (2) the ability to improve estimates of the exposure point concentration by exploiting the geospatial information present in the data. The second contribution is particularly valuable when exposure estimates must be derived from small data sets, which is often the case in environmental risk assessment. This article addresses two topics related to the use of geostatistics in human and ecological risk assessments performed at hazardous waste sites: (1) the importance of assessing model assumptions when using geostatistics and (2) the use of geostatistics to improve estimates of the exposure point concentration (EPC) in the limited data scenario. The latter topic is approached here by comparing design-based estimators that are familiar to environmental risk assessors (e.g., Land's method) with geostatistics, a model-based estimator. In this report, we summarize the basics of spatial weighting of sample data, kriging, and geostatistical simulation. We then explore the two topics identified above in a case study, using soil lead concentration data from a Superfund site (a skeet and trap range). We also describe several areas where research is needed to advance the use of geostatistics in environmental risk assessment.     

Functional regression concurrent model with spatially correlated errors: application to rainfall ground validation

In this paper, we give an extension of the functional regression concurrent model to the case of spatially correlated errors. We propose estimating the spatial correlation structure by using functional geostatistics. The estimation of the regression parameters is carried out by feasible generalized least squares. This modeling approach is motivated by the problem of validating rainfall data retrieved from satellite sensors. In this sense, we use the methodology to study the relationship between satellite and ground rainfall time series recorded in 82 weather stations from Department of Valle del Cauca, Colombia. The model obtained allows predicting pentadal rainfall curves in many sites of the region of interest by using as input the satellite information. A residual analysis shows a good performance of the methodology proposed.     

Flexible spatio-temporal stationary variogram models

In this paper we propose a generalization of the Shapiro and Botha (1991) approach that allows one to obtain flexible spatio-temporal stationary variogram models. It is shown that if the weighted least squares criterion is chosen, the fitting of such models to pilot estimations of the variogram can be easily carried out by solving a quadratic programming problem. The work also includes an application to real data and a simulation study in order to illustrate the performance of the proposed space-time dependency modeling.     

Non-stationary partition modeling of geostatistical data for malaria risk mapping

The most common assumption in geostatistical modeling of malaria is stationarity, that is spatial correlation is a function of the separation vector between locations. However, local factors (environmental or human-related activities) may influence geographical dependence in malaria transmission differently at different locations, introducing non-stationarity. Ignoring this characteristic in malaria spatial modeling may lead to inaccurate estimates of the standard errors for both the covariate effects and the predictions. In this paper, a model based on random Voronoi tessellation that takes into account non-stationarity was developed. In particular, the spatial domain was partitioned into sub-regions (tiles), a stationary spatial process was assumed within each tile and between-tile correlation was taken into account. The number and configuration of the sub-regions are treated as random parameters in the model and inference is made using reversible jump Markov chain Monte Carlo simulation. This methodology was applied to analyze malaria survey data from Mali and to produce a country-level smooth map of malaria risk.