By Hengl, Tomislav
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Extra info for A Practical Guide to Geostatistical Mapping of Environmental Variables
Sample text
C(sn , s1 ) · · · C(sn , sn ) 1 C(s0 , sn ) 1 ··· 1 0 1 w1 (s0 ) .. . 5) ϕ where ϕ is the so-called Langrange multiplier . In addition to estimation of values at new locations, a statistical spatial prediction technique offers a measure of associated uncertainty of making these estimations by using a given model. e. the estimated variance of the prediction error. 5). As you can notice, outputs from any statistical prediction model are always two maps: (1) predictions and (2) prediction variance.
24) it is obvious that the precision of the technique will be maximized if the within-unit variation is infinitely small. Likewise, if the within-unit variation is as high as the global variability, the predictions will be as bad as predicting by taking any value from the normal distribution. Another approach to make predictions from polygon maps is to use multiple regression. In this case, the predictors (mapping units) are used as indicators: zˆ(s0 ) = ˆb1 · MU 1 (s0 ) + . . 23) are in fact equivalent.
Distance’ of the new observation from the centre of the feature space [q(s0 ) − q¯]. 3 Statistical spatial prediction models 23 So in general, if the model is linear, we can decrease the prediction variance if we increase the spreading of the points in features space. 6). , 1996), R2 indicates amount of variance explained by model, whereas Ra2 adjusts for the number of variables (p) used. 85 is already a very satisfactory solution and higher values will typically only mean over-fitting of the data (Park and Vlek, 2002).