Hierarchical clustering of spatially correlated functional data

Classification problems of functional data arise naturally in many applications. Several approaches have been considered for solving the problem of funding groups based on functional data. In this paper we are interested in detecting groups when the functional data are spatially correlated. Our methodology allows to find spatially homogeneous groups of sites when the observations at each sampling location consist of samples of random functions. In univariable and multivariable geostatistics various methods of incorporating spatial information into the clustering analysis have been considered. Here we extend these methods to the functional context in order to fulfill the task of clustering spatially correlated curves. In our approach we initially use basis functions to smooth the observed data and then we weight the dissimilarity matrix among curves by either the trace-variogram or the multivariable variogram calculated with the coeficients of the basis functions. As an illustration the methodology is applied to a real data set corresponding to average daily temperatures measured at 35 Canadian weather stations

Interpolating point spread function anisotropy

Planned wide-field weak lensing surveys are expected to reduce the statistical errors on the shear field to unprecedented levels. In contrast, systematic errors like those induced by the convolution with the point spread function (PSF) will not benefit from that scaling effect and will require very accurate modeling and correction. While numerous methods have been devised to carry out the PSF correction itself, modeling of the PSF shape and its spatial variations across the instrument field of view has, so far, attracted much less attention. This step is nevertheless crucial because the PSF is only known at star positions while the correction has to be performed at any position on the sky. A reliable interpolation scheme is therefore mandatory and a popular approach has been to use low-order bivariate polynomials. In the present paper, we evaluate four other classical spatial interpolation methods based on splines (B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and ordinary Kriging (OK). These methods are tested on the Star-challenge part of the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and are compared with the classical polynomial fitting (Polyfit). We also test all our interpolation methods independently of the way the PSF is modeled, by interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are known exactly at star positions). We find in that case RBF to be the clear winner, closely followed by the other local methods, IDW and OK. The global methods, Polyfit and B-splines, are largely behind, especially in fields with (ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all interpolators reach a variance on PSF systematics $\sigma_{sys}^2$ better than the $1\times10^{-7}$ upper bound expected by future space-based surveys, with the local interpolators performing better than the global ones

Assessment of Ore Grade Estimation Methods for Structurally Controlled Vein Deposits - A Review

Resource estimation techniques have upgraded over the past couple of years, thereby improving resource estimates. The classical method of estimation is less used in ore grade estimation than geostatistics (kriging) which proved to provide more accurate estimates by its ability to account for the geology of the deposit and assess error. Geostatistics has therefore been said to be superior over the classical methods of estimation. However, due to the complexity of using geostatistics in resource estimation, its time-consuming nature, the susceptibility to errors due to human interference, the difficulty in applying it to deposits with few data points and the difficulty in using it to estimate complicated deposits paved the way for the application of Artificial Intelligence (AI) techniques to be applied in ore grade estimation. AI techniques have been employed in diverse ore deposit types for the past two decades and have proven to provide comparable or better results than those estimated with kriging. This research aimed to review and compare the most commonly used kriging methods and AI techniques in ore grade estimation of complex structurally controlled vein deposits. The review showed that AI techniques outperformed kriging methods in ore grade estimation of vein deposits.   Keywords: Artificial Intelligence, Neural Networks, Geostatistics, Kriging, Mineral Resource, Grad

Predicting House Prices with Spatial Dependence: A Comparison of Alternative Methods

This paper compares alternative methods for taking spatial dependence into account in house price prediction. We select hedonic methods that have been reported in the literature to perform relatively well in terms of ex-sample prediction accuracy. Because differences in performance may be due to differences in data, we compare the methods using a single data set. The estimation methods include simple OLS, a two-stage process incorporating nearest neighbors’ residuals in the second stage, geostatistical, and trend surface models. These models take into account submarkets by adding dummy variables or by estimating separate equations for each submarket. Based on data for approximately 13,000 transactions from Louisville, Kentucky, we conclude that a geostatistical model with disaggregated submarket variables performs best.

Summary characteristics for multivariate function-valued spatial point process attributes

Prompted by modern technologies in data acquisition, the statistical analysis of spatially distributed function-valued quantities has attracted a lot of attention in recent years. In particular, combinations of functional variables and spatial point processes yield a highly challenging instance of such modern spatial data applications. Indeed, the analysis of spatial random point configurations, where the point attributes themselves are functions rather than scalar-valued quantities, is just in its infancy, and extensions to function-valued quantities still remain limited. In this view, we extend current existing first- and second-order summary characteristics for real-valued point attributes to the case where in addition to every spatial point location a set of distinct function-valued quantities are available. Providing a flexible treatment of more complex point process scenarios, we build a framework to consider points with multivariate function-valued marks, and develop sets of different cross-function (cross-type and also multi-function cross-type) versions of summary characteristics that allow for the analysis of highly demanding modern spatial point process scenarios. We consider estimators of the theoretical tools and analyse their behaviour through a simulation study and two real data applications.Comment: submitted for publicatio

Prediction of spatial distribution for some land use allometric characteristics in land use planning models with geostatistic and Geographical Information System (GIS) (Case study: Boein and Miandasht, Isfahan Province, Iran)

Although traditional census can present unbiased information about different land uses, it is spatial independent and do not present particular  information about spatial distribution of studied characteristic. In this study, we used geostatistic and Geographical Information System (GIS) to estimate some different land uses allometric characteristics in Isfahan Province (Iran). Thus, samples information was surveyed considering their geographic position in the studied area. After optimizing variogram parameters,  empirical variogram was prepared to investigate spatial structure of different land uses allometric characteristics. Our results confirme that spatial  structure for the quantitative characteristics of different land uses has a moderate degree of spatial correlation, except for type variable that has no spatial structure. Nugget effect for variogram obtained from the quantitative characteristics of different land uses was equal to 35 to 64%. We used ordinary Kriging for preparing Kriging map and Kriging standard deviation of different land uses. Also, we used geostatistic and GIS to compare geostatistical and algebraic interpolation methods and nine different interpolation methods (Kriging, local polynomial methods, inverse distance weighted, radial basis functions, global polynomial, moving average  weighted, natural neighbor, nearest neighbor and triangulation with Linear Interpolation) were investigated. Spatial distribution of different land uses quantitative characteristics were validated with ordinary Kriging and algebraic methods. Our results confirm that ordinary Kriging has more accuracy than other methods for spatial prediction of different land uses quantitative characteristics.Key words: Geostatistic, interpolation method, land use allometric  characteristics, Kriging