Empirical Bayesian Kriging (Geostatisical Analyst)

License Level:BasicStandardAdvanced


Empirical Bayesian Kriging is an interpolation method that accounts for the error in estimating the underlying semivariogram through repeated simulations.

What is Empirical Bayesian Kriging?



EmpiricalBayesianKriging_ga (in_features, z_field, {out_ga_layer}, {out_raster}, {cell_size}, {transformation_type}, {max_local_points}, {overlap_factor}, {number_semivariograms}, {search_neighborhood}, {output_type}, {quantile_value}, {threshold_type}, {probability_threshold})
ParameterExplanationData Type

The input point features containing the z-values to be interpolated.

Feature Layer

Field that holds a height or magnitude value for each point. This can be a numeric field or the Shape field if the input features contain z-values or m-values.


The geostatistical layer produced. This layer is required output only if no output raster is requested.

Geostatistical Layer

The output raster. This raster is required output only if no output geostatistical layer is requested.

Raster Dataset

The cell size at which the output raster will be created.

This value can be explicitly set under Raster Analysis from the Environment Settings. If not set, it is the shorter of the width or the height of the extent of the input point features, in the input spatial reference, divided by 250.

Analysis Cell Size

Type of transformation to be applied to the input data.

  • NONE Do not apply any transformation. This is the default.
  • EMPIRICALMultiplicative Skewing transformation with Empirical base function.
  • LOGEMPIRICALMultiplicative Skewing transformation with Log Empirical base function. All data values must be positive.

The input data will automatically be divided into groups that do not have more than this number of points.


A factor representing the degree of overlap between local models (also called subsets). Each input point can fall into several subsets, and the overlap factor specifies the average number of subsets that each point will fall into. A high value of the overlap factor makes the output surface smoother, but it also increases processing time. Typical values vary between 0.01 and 5.


The number of simulated semivariograms.


Defines which surrounding points will be used to control the output. Standard is the default.

This is a Search Neighborhood class SearchNeighborhoodStandardCircular and SearchNeighborhoodSmoothCircular.


  • Radius—The length of the radius of the search circle.
  • Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.
  • Maximum neighbors—The maximum number of neighbors that will be used to estimate the value at the unknown location.
  • Minimum neighbors—The minimum number of neighbors that will be used to estimate the value at the unknown location.
  • Sector type—The geometry of the neighborhood.
    • One sector—Single ellipse.
    • Four sectors—Ellipse divided into four sectors.
    • Four sectors shifted—Ellipse divided into four sectors and shifted 45 degrees.
    • Eight sectors—Ellipse divided into eight sectors.


  • Radius—The length of the radius of the search circle.
  • Smoothing factor—The Smooth Interpolation option creates an outer ellipse and an inner ellipse at a distance equal to the Major Semiaxis multiplied by the Smoothing factor. The points that fall outside the smallest ellipse but inside the largest ellipse are weighted using a sigmoidal function with a value between zero and one.
Geostatistical Search Neighborhood

Surface type to store the interpolation results.

  • PREDICTIONPrediction surfaces are produced from the interpolated values.
  • PREDICTION_STANDARD_ERROR Standard Error surfaces are produced from the standard errors of the interpolated values.
  • PROBABILITYProbability surface of values exceeding or not exceeding a certain threshold.
  • QUANTILEQuantile surface depicting the chance that a prediction is above a certain value.

The quantile value for which the output raster will be generated.


Determines whether the probability values exceed the threshold value or not.

  • EXCEEDProbability values exceed the threshold. This is the default.
  • NOT_ EXCEED Probability values will not exceed the threshold.

The probability threshold value. If left empty, the median of the input data will be used.


Code Sample

EmpiricalBayesianKriging example 1 (Python window)

Interpolate a series of point features onto a raster.

import arcpy
arcpy.EmpiricalBayesianKriging_ga("ca_ozone_pts", "OZONE", "outEBK", "C:/gapyexamples/output/ebkout",
                                  10000, "NONE", 50, 0.5, 100,
                                  arcpy.SearchNeighborhoodStandardCircular(300000, 0, 15, 10, "ONE_SECTOR"),
                                  "PREDICTION", "", "", "")
EmpiricalBayesianKriging example 2 (stand-alone script)

Interpolate a series of point features onto a raster.

# Name: EmpiricalBayesianKriging_Example_02.py
# Description: Bayesian kriging approach whereby many models created around the
#   semivariogram model estimated by the restricted maximum likelihood algorithm is used.
# Requirements: Geostatistical Analyst Extension
# Author: Esri

# Import system modules
import arcpy

# Set environment settings
arcpy.env.workspace = "C:/gapyexamples/data"

# Set local variables
inPointFeatures = "ca_ozone_pts.shp"
zField = "ozone"
outLayer = "outEBK"
outRaster = "C:/gapyexamples/output/ebkout"
cellSize = 10000.0
transformation = "NONE"
maxLocalPoints = 50
overlapFactor = 0.5
numberSemivariograms = 100
# Set variables for search neighborhood
radius = 300000
smooth = 0.6
searchNeighbourhood = arcpy.SearchNeighborhoodSmoothCircular(radius, smooth)
outputType = "PREDICTION"
quantileValue = ""
thresholdType = ""
probabilityThreshold = ""
# Check out the ArcGIS Geostatistical Analyst extension license

# Execute EmpiricalBayesianKriging
arcpy.EmpiricalBayesianKriging_ga(inPointFeatures, zField, outLayer, outRaster,
                                  cellSize, transformation, maxLocalPoints, overlapFactor, numberSemivariograms,
                                  searchNeighbourhood, outputType, quantileValue, thresholdType, probabilityThreshold)


Related Topics

Licensing Information

ArcGIS for Desktop Basic: Requires Geostatistical Analyst
ArcGIS for Desktop Standard: Requires Geostatistical Analyst
ArcGIS for Desktop Advanced: Requires Geostatistical Analyst