o What can be estimated ? Estimation. ⢠Punctual estimation. ⢠Block average estimation. Estimate the value Z. 0 at the nodes of. Geostatistics & RGeostats. 2.
Estimation o What can be estimated ? Punctual estimation Block average estimation
Estimate the value Z0 at the nodes of a regular grid Samples Estimate the average of the variable Z over the block
Geostatistics & RGeostats
2
Estimation o Linear estimation techniques Linear estimator: • Each estimation is obtained as a linear combination of the values measured at sample points
Several linear interpolation techniques: • Moving average • Inverse distance (closest point) • Inverse distance
Properties of the estimation: • Smoothness • Unbiasedness • Exact interpolation
Geostatistics & RGeostats
3
Interpolation o Illustration Exhaustive data set (reality) Irregular sampling used as data For each method, represent the estimation as a map and along a section >=3 2.7 2.4 2.1 1.8 1.5 1.2 0.9 0.6 0.3 0 -0.3 -0.6 -0.9 -1.2 -1.5 -1.8 -2.1 -2.4 -2.7 radius 33.3%
33.3% 37.0%
σ = 0.45 2
33.3% 25.7%
48.7% Geostatistics & RGeostats
26.0% 25.7%
σ 2 = 0.526
σ = 0.48
37.0%
2
50.0%
σ 2 = 0.537
50.0% 36
Cross-validation o Principle At each data point:
Zα*0 =
• Suppress the sample value • Estimate its value by Kriging • Compare real to estimated values
Statistics on: • Error:
• Normalized error
Geostatistics & RGeostats
λα Zα ∑ α α ≠
0
ε α = Zα* − Zα 0
ε αR =
Zα*0 − Zα
σα
37
Neighborhood o Principle Kriging considers available samples in the system When too many samples, kriging system becomes very large and may become difficult to invert (unstable, slow) Kriging weights of peripheral points are small: could they be neglected? Neighborhood: Unique: Take all data available Moving: Select the most appropriate subset of neighboring samples • By number • By maximum distance • By angular sector
Page 1 .... Calculate: ⢠The mean and variance. ⢠The experimental variogram for the lag 1m, 2m and 3m. + + + + + + + + + + + + + ... Rank Npairs Distance Value.
Jun 2, 2012 - the R distribution library (if you succeeded installing RGeoS using the admin- istrator privileges) or in a private directory. This instruction can be ...
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Getting Started manual for installation of RGeostats package. 1 History of the .... First file for future use. The contents of the .First file ... l s ( pos=2). Another way to ...
o Why multivariate geostatistics. Introduction. ⢠Highlight structural relationship between variables. ⢠Improve the estimation of one variable using auxiliary ...
a spherical component with a range of 5.2 and a sill equal to 2.4 ... This model is sampled by calculating an experimental variogram with 100 lags of 0.1 each.
Feb 5, 2013 - RGeoS Manual. Didier RENARD. February 5 th .... also be parametrized in the .First file for future use. ... l s ( pos=7). Another way to learn about ...
o Principles (1/2). Geostatistics and RGeostats. ⢠Basic principles of Geostatistics: ⢠Statistics ... Can be used for teaching and for non-commercial purposes.
Oct 3, 2014 - with virtualization is ok) to connect to the ICES network, and also to have R (freely downloadable from http://www.r-project.org/) installed prior to ...
Oct 18, 2018 - Computes 3 multiple-site dissimilarities accounting for the spatial turnover and the nestedness com- ponents of beta diversity, and the sum of ...
Jun 7, 2016 - 2015) sim01 simulated haploid genotypic dataset exhibiting clear spatial ..... Sp. ## 1 -0.1664517 0.1898369. The variogram is the sum of the .... Altitudinal Gradient in the French Alps.â Annals of Forest Science 72: 517â27.
out$rand. Frequency. â4. â2. 0. 2. 4. 0. 5. 10. 15. It is interesting to add the vertical lines corresponding to the observed value (in red) and the quantile values for ...
Journal of Statistical Software .... scatter plots for a better understanding of the data. ..... In âProceedings of the 76th Convention of the American Psychological.
Jul 29, 2008 - Introduction ... for testing forecasting methods. ... the exponential smoothing approach (in Section 2) and the ARIMA ... framework incorporating procedures for model selection was not ..... Unlike state space models with multiple ....
The package downloadable file is ... since case event data are used, the method is free from map partition. Finally ... detection, Biometrics 57 (2001) 577â583.
Apr 26, 2012 - This measure has been defined by INSEE (Institut National de la Statistique et des Ãtudes ... For each site (for each zone), the data set must contain the cartesian coordinates of ...... R package version 0.5-43, URL http://CRAN.
Type of article: Full length article for Ecology and Evolution ... deforestation and carbon dioxide emissions are necessary. Although ... Here, we propose an innovative approach using novel computational and statistical tools, including ... 41 1 Intr
scribe a project for creating an open-source S-PLUS/R pack- .... son 1960), which combines forward and backward steps. .... and continues in this fashion.
Apr 26, 2012 - (2001) develop SAGE, a software system held in the ArcInfo GIS, with ..... The reader can get more details about the use of the options in the ...
Jul 10, 2006 - Title Arbitrarily Shaped Multiple Spatial Cluster Detection for Case Event Data. .... finally tests the significativity of those potential clusters. Value.
