ArcGIS Tutorial: What is experiential Bayesian gold law?

　　Brief introduction

Empirical Bayesian kriging (EBK) is a geostatistical interpolation method that automates the most difficult steps in the process of building an effective kriging model. The other geostatistical methods in the G-Analyst require you to manually adjust the parameters to receive accurate results, while the EBK can automatically calculate these parameters by constructing subsets and simulation processes.

Empirical Bayesian Gold method differs from other methods of gold-based method by estimating the underlying semivariogram to illustrate the errors introduced. Other methods of the gold method the Semivariogram is computed by the known data location, and the single-half mutation function is used to predict the unknown position; This process implicitly assumes that the estimated Semivariogram is the true semivariogram of the interpolated region. Because the uncertainty of semivariogram estimation is not taken into account, the standard error of prediction is underestimated by other methods of gold.

Empirical Bayesian Gold method is provided as a geoprocessing tool in the Geostatistical Wizard.

　　Pros and cons

　　Advantages

Requires very little interactive modeling;

The prediction standard error is more accurate than the other methods of the gold.

Can accurately predict the general degree of unstable data;

For small datasets, it is more accurate than other kriging methods;

　Disadvantages

1, processing time will increase with the number of input points, the size of the subset or the overlap coefficient increases rapidly. Applying transforms also increases processing time. The parameters are described below

2. Processing speed is slower than other methods of gold, especially when the output is a grid.

3, cooperative kriging and anisotropy are not available.

, a few parameters in the Semivariogram model limit the custom functionality. Other methods of the method of gold are used to provide a variety of options for semivariogram models.

5, log experience transformation is particularly sensitive to outliers. If you use the transform with data that contains outliers, you may get predictions that are greater than or less than the number of orders of magnitude of the input point values. This parameter is described in the "Transformations" section below.

　　Estimation of semi-variable function

Unlike other kriging (using weighted least squares), the semivariogram parameters in EBK are estimated using the limited maximum likelihood (REML) method. Because REML has computational limitations on large datasets, the input data is first divided into overlapping subsets of a specific size (the default is 100 points per subset). In each subset, the Semivariogram is estimated as follows:

1, the semivariogram is estimated by the data in the sub-set.

2. Use this semivariogram as a model, and the new data will be simulated unconditionally at each input location of the subset.

3, the new Semivariogram is estimated by the simulated data.

4. Repeat step 2 and step 3 for the specified number of times. In each repetition, the semivariogram estimated in step 1 is used to simulate a new set of data at the input location, and the simulated data is used to estimate the new semivariogram.

This process creates a large number of semivariogram for each subset, and when you draw them together, the result is a distribution of the semivariogram that is colored by density (the darker the blue, the more the Semivariogram through that region). In addition, the median value of the distribution is represented by a solid red line, and the 25% and 75% percent values are represented by a dashed red, as shown in.

　　

The number of semivariogram simulations in each sub-set defaults to 100, where each semivariogram is an estimate of the true semivariogram of a subset.

For each location, a unique semivariogram distribution is used to generate the prediction, which is calculated by a weighted synthesis of the distribution of the surrounding subset; The closer the subset distance is predicted, the higher the given weight.

　　Kriging model

Empirical Bayesian kriging differs from other methods of geostatistical Analyst in that it uses the intrinsic 0-order random function (IRF-0) as the model of the notation.

Other kriging models assume that the process follows an overall average (or a specified trend), and that the various changes revolve around the average. Larger deviations are pulled back to the average value, so the values are not too large. However, the EBK will not show a trend towards the overall average, so the larger deviations are more likely to become smaller.

　　Semi-variant function model

For a given distance h, the empirical Bayesian method uses the following form of Semivariogram:

Gamma (h) = Nugget + b|h|α

The Nugget value and B (slope) must be positive, while α (power) must be between 0.25 and 1.75. Under these limits, use REML to estimate parameters. The Semivariogram model does not have a range or abutment parameter because the function has no upper bound. In EBK, the empirical distributions of parameter estimates can be analyzed because multiple semivariogram are estimated at each location. Click the block gold value, slope, or Power tab to display the distribution of the associated parameters. Shows the Semivariogram parameter distributions for the simulated semivariogram shown in the previous picture:

　　

Click a different location on the preview surface to display the Semivariogram distribution and Semivariogram parameter distributions for the new location. If the distribution does not change significantly within the data domain, the data is in a global steady state. Distributions should be smoothed across the entire data range, but if there is a large change in the distribution of the shorter distances, the increase in the value of the overlap factor can smooth the distribution of the transition.

　　Transform

Empirical Bayesian method provides two basic distributions for multiplicative skew normal score transformation: Empirical method and logarithmic empirical method. Log experience transformation requires that all data values be positive to ensure that all predictions are positive. It applies to data such as rainfall, which cannot be negative.

　　

If you apply a transform, a simple kriging model will be used instead of IRF-0, and the semivariogram will fit into the exponential semivariogram model. As a result of these changes, the parameter distribution is changed to the block gold value, the bias base value, and the change range value. In addition, a Transform tab appears in which to display the distribution of the fitted transformation (one for each simulation). As with the Semivariogram tab, the transformation distribution is colored by density and provides a sub-digit line.

　　

　　New parameters of empirical Bayesian gold method

Empirical Bayesian method uses three parameters that are not present in the other methods of the Gram-gold:

1. Subset Size-Specify the number of points in each sub-set. The larger the subset, the longer the EBK computation takes.

2. Overlap Factor-Specifies the degree of overlap between subsets. Each input point can fall into multiple subsets, and the overlap factor specifies the average number of subsets to which the points fall. For example, the overlap factor of 1.5 means that approximately half of the points are used in a subset, and the other half of the points are used in two sub-sets. The larger the value of the overlap factor, the smoother the output surface, but it also increases processing time.

3. Number of simulations-Specifies the number of semivariogram that will be simulated for each subset. The more simulations are generated, the more accurate the predictions will be, but the processing time will also increase.

ArcGIS Tutorial: What is experiential Bayesian gold law?