[1] During the last decade one has witnessed an increasing interest in assessing health risks caused by exposure to contaminants present in the soil, air, and water. A key component of any exposure study is a reliable model for the space-time distribution of pollutants. This paper compares the performances of multi-Gaussian and indicator kriging for modeling probabilistically the spatial distribution of arsenic concentrations in groundwater of southeast Michigan, accounting for arsenic data collected at private residential wells and the hydrogeochemistry of the area. The arsenic data set, which was provided by the Michigan Department of Environmental Quality (MDEQ), includes measurements collected between 1993 and 2002 at 8212 different wells. Factorial kriging was used to filter the short-range spatial variability in arsenic concentration, leading to a significant increase (17-65%) in the proportion of variance explained by secondary information, such as type of unconsolidated deposits and proximity to Marshall Sandstone subcrop. Cross validation of well data shows that accounting for this regional background does not improve the local prediction of arsenic, which reveals the presence of unexplained sources of variability and the importance of modeling the uncertainty attached to these predictions. Slightly more precise models of uncertainty were obtained using indicator kriging. Well data collected in 2004 were compared to the prediction model and best results were found for soft indicator kriging which has a mean absolute error of 5.6 mg/L. Although this error is large with respect to the USEPA standard of 10 mg/L, it is smaller than the average difference (12.53 mg/L) between data collected at the same well and day, as reported in the MDEQ data set. Thus the uncertainty attached to the sampled values themselves, which arises from laboratory errors and lack of information regarding the sample origin, contributes to the poor accuracy of the geostatistical predictions in southeast Michigan.Citation: Goovaerts, P., G. AvRuskin, J. Meliker, M. Slotnick, G. Jacquez, and J. Nriagu (2005), Geostatistical modeling of the spatial variability of arsenic in groundwater of southeast Michigan, Water Resour. Res., 41, W07013,

This paper describes a k nearest neighbour statistic sensitive to the pattern of cases expected of space-time clusters of health events. The Knox and Mantel tests are frequently used for space-time clustering but have two disadvantages. First, the selection of critical space-time distances for the Knox test and of a data transformation for the Mantel test is subjective. Second, the Mantel statistic is the sum of the products of space and time distances, is linear in form, and is not sensitive to non-linear associations between small space and time distances expected of contagious processes. The k nearest neighbour statistic is the number of case pairs that are k nearest neighbours in both space and time, and is evaluated under the null hypothesis of independent space and time nearest neighbour relationships. The test was applied to simulated and real data and compared to the Knox and Mantel tests using statistical power comparisons. The k nearest neighbour test proved sensitive to the space-time interaction pattern expected of disease clusters, does not require parameters (such as critical distances) to be estimated from the data, and may be used to test hypotheses about the spatial and temporal scale of the cluster process. The method addresses significant weaknesses in existing space-time cluster tests and should prove useful in the quantification and evaluation of clusters of human health events. Additional research is needed to further document the power of the test under different cluster processes.

Geographic boundary analysis is a relatively new approach unfamiliar to many spatial analysts. It is best viewed as a technique for de®ning objects ± geographic boundaries ± on spatial ®elds, and for evaluating the statistical signi®cance of characteristics of those boundary objects. This is accomplished using null spatial models representative of the spatial processes expected in the absence of boundary-generating phenomena. Close ties to the object-®eld dialectic eminently suit boundary analysis to GIS data. The majority of existing spatial methods are ®eld-based in that they describe, estimate, or predict how attributes (variables de®ning the ®eld) vary through geographic space. Such methods are appropriate for ®eld representations but not object representations. As the object-®eld paradigm gains currency in geographic information science, appropriate techniques for the statistical analysis of objects are required. The methods reviewed in this paper are a promising foundation. Geographic boundary analysis is clearly a valuable addition to the spatial statistical toolbox. This paper presents the philosophy of, and motivations for geographic boundary analysis. It de®nes commonly used statistics for quantifying boundaries and their characteristics, as well as simulation procedures for evaluating their signi®cance. We review applications of these techniques, with the objective of making this promising approach accessible to the GIS-spatial analysis community. We also describe the implementation of these methods within geographic boundary analysis software: GEM.

We generated numerous simulated gene-frequency surfaces subjected to 200 generations of isolation by distance with, in some cases, added migration or selection. From these surfaces we assembled six data sets comprising from 12 to 15 independent allele-frequency surfaces, to simulate biologically plausible population samples. The purpose of the study was to investigate whether spatial autocorrelation analysis will correctly infer the microevolutionary processes involved in each data set. The correspondence between the simulated processes and the inferences made concerning them is close for five of the six data sets. Errors in inference occurred when the effect of migration was weak, due to low gene frequency differential or low migration strength; when selection was weak and against a background with a complex pattern; and when a random process-isolation by distance-was the only one acting. Spatial correlograms proved more sensitive to detecting trends than inspection of gene-frequency surfaces by the human eye. Joint interpretation of the correlograms and their clusters proved most reliable in leading to the correct inference. The inspection and clustering of surfaces were useful for determining directional components. Because this method relies on common patterns across loci, as many gene frequencies as feasible should be used. We recommend spatial autocorrelation analysis for the detection of microevolutionary processes in natural populations.