scholarly journals Discussion on Competition for Spatial Statistics for Large Datasets

2021 ◽  
Author(s):  
Roman Flury ◽  
Reinhard Furrer
Keyword(s):  
Spatial Statistics ◽  
Covariance Function ◽  
Likelihood Function ◽  
Large Datasets ◽  
Missing Observations ◽  
Covariance Model ◽  
Compactly Supported ◽  
Covariance Tapering ◽  
Simple Kriging ◽  
Estimated Parameters

AbstractWe discuss the experiences and results of the AppStatUZH team’s participation in the comprehensive and unbiased comparison of different spatial approximations conducted in the Competition for Spatial Statistics for Large Datasets. In each of the different sub-competitions, we estimated parameters of the covariance model based on a likelihood function and predicted missing observations with simple kriging. We approximated the covariance model either with covariance tapering or a compactly supported Wendland covariance function.

Competition on Spatial Statistics for Large Datasets

2021 ◽  
Author(s):  
Huang Huang ◽  
Sameh Abdulah ◽  
Ying Sun ◽  
Hatem Ltaief ◽  
David E. Keyes ◽  
...  
Keyword(s):  
Spatial Statistics ◽  
Large Datasets

scholarly journals Interval maximum likelihood inversion for well logging data and statistical properties of estimated parameters

2021 ◽  
Author(s):  
László Balázs
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Function ◽  
Extremum Problem ◽  
Statistical Properties ◽  
Matrix Composition ◽  
Estimated Parameters ◽  
Petrophysical Model ◽  
Zone Parameters ◽  
Zone Depth ◽  
Formation Water Resistivity

AbstractDuring the conventional petrophysical interpretation fixed (predefined) zone parameters are applied for every interpretation zone (depth intervals). Their inclusion in the inversion process requires the extension of a likelihood function for the whole zone. This allows to define the extremum problem for fitting the parameter set to the full interval petrophysical model of the layers crossed by the well, both for the parameters associated with the depth points (e.g. porosity, saturations, rock matrix composition etc.) and for the zone parameters (e.g. formation water resistivity, cementation factor etc.). In this picture the parameters form a complex coupled and correlated system. Even the local parameters associated with different depths are coupled through the zone parameter change. In this paper, the statistical properties of the coupled parameter system are studied which fitted by the Interval Maximum Likelihood (ILM) method. The estimated values of the parameters are coupled through the likelihood function and this determines the correlation between them.

scholarly journals LÉVY-BASED ERROR PREDICTION IN CIRCULAR SYSTEMATIC SAMPLING

2013 ◽  
Vol 32 (2) ◽  
pp. 117 ◽  
Author(s):  
Kristjana Ýr Jónsdóttir ◽  
Eva B. Vedel Jensen
Keyword(s):  
Stochastic Process ◽  
Statistical Inference ◽  
Covariance Function ◽  
Kernel Smoothing ◽  
Stationary Stochastic Process ◽  
Systematic Sampling ◽  
Error Prediction ◽  
Model Parameters ◽  
Covariance Model ◽  
Measurement Function

In the present paper, Lévy-based error prediction in circular systematic sampling is developed. A model-based statistical setting as in Hobolth and Jensen (2002) is used, but the assumption that the measurement function is Gaussian is relaxed. The measurement function is represented as a periodic stationary stochastic process X obtained by a kernel smoothing of a Lévy basis. The process X may have an arbitrary covariance function. The distribution of the error predictor, based on measurements in n systematic directions is derived. Statistical inference is developed for the model parameters in the case where the covariance function follows the celebrated p-order covariance model.

scholarly journals Tomography of the ionospheric electron density with geostatistical inversion

2015 ◽  
Vol 33 (8) ◽  
pp. 1071-1079 ◽  
Author(s):  
D. Minkwitz ◽  
K. G. van den Boogaart ◽  
T. Gerzen ◽  
M. Hoque
Keyword(s):  
Electron Density ◽  
Signal Propagation ◽  
Global Navigation Satellite Systems ◽  
Electron Content ◽  
Covariance Model ◽  
Spatial Covariance ◽  
Total Electron ◽  
Satellite Systems ◽  
Simple Kriging ◽  
Global Navigation Satellite

Abstract. In relation to satellite applications like global navigation satellite systems (GNSS) and remote sensing, the electron density distribution of the ionosphere has significant influence on trans-ionospheric radio signal propagation. In this paper, we develop a novel ionospheric tomography approach providing the estimation of the electron density's spatial covariance and based on a best linear unbiased estimator of the 3-D electron density. Therefore a non-stationary and anisotropic covariance model is set up and its parameters are determined within a maximum-likelihood approach incorporating GNSS total electron content measurements and the NeQuick model as background. As a first assessment this 3-D simple kriging approach is applied to a part of Europe. We illustrate the estimated covariance model revealing the different correlation lengths in latitude and longitude direction and its non-stationarity. Furthermore, we show promising improvements of the reconstructed electron densities compared to the background model through the validation of the ionosondes Rome, Italy (RO041), and Dourbes, Belgium (DB049), with electron density profiles for 1 day.

Discussion on Competition for Spatial Statistics for Large Datasets

2021 ◽  
Author(s):  
Lewis R. Blake ◽  
Olga Khaliukova ◽  
Alexander Pinard ◽  
Douglas Nychka ◽  
Dorit Hammerling ◽  
...  
Keyword(s):  
Spatial Statistics ◽  
Large Datasets

Assessment of Tscherning-Rapp covariance in Earth gravity modeling using gravity gradient and GPS/leveling observations

2020 ◽  
Author(s):  
Hadi Heydarizadeh Shali ◽  
Sabah Ramouz ◽  
Abdolreza Safari ◽  
Riccardo Barzaghi
Keyword(s):  
Gravity Field ◽  
Covariance Function ◽  
Data Distribution ◽  
Gravity Modeling ◽  
Gravity Gradient ◽  
Control Points ◽  
Covariance Model ◽  
Gps Leveling ◽  
And Control ◽  
Empirical Covariance

<p>Determination of Earth’s gravity field in a high accuracy needs different complementary data and also methods to combine these data in an optimized procedure. Newly invented resources such as GPS, GRACE, and GOCE provide various data with different distribution which makes it possible to reach this aim. Least Squares Collocation (LSC) is one of the methods that help to mix different data types via covariance function which correlates the different involved parameters within the procedure. One way to construct such covariance functions is involving two steps within the remove-compute-restore (RCR) procedure: first, calculation of an empirical covariance function from observations which the gravitational effects of global gravity field (Long-wavelength) and topography/bathymetry have been subtracted from it and then fitting the Tscherning–Rapp analytical covariance model to the empirical one. According to the corresponding studies, the accuracy of LSC is directly related to the ability to localize the covariance function which itself depends on the data distribution. In this study, we have analyzed the data distribution and geometrically fitting factors, on GPS/Leveling and GOCE gradient data by considering the various case studies with different data distributions. To make the assessment of the covariance determination possible, the residual observations were divided into two datasets namely, observations and control points. The observations point served as input data within the LSC procedure using the Tscherning – Rapp covariance model and the control points used to evaluate the accuracy of the LSC in gravity gradient, gravity anomaly, and geoid predicting and then the covariance estimation. The results of this study show that the Tscherning-Rapp (1974) covariance has different outcomes over different quantities. For example, it models accurate enough the empirical covariance of gradient gravity but requires more analysis for gravity anomalies and GPS/Leveling quantities to reach the optimized results in terms of STD of difference between the computed and control points.</p>

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