Empirical Bayesian Kriging (Geostatisical Analyst)
Summary
Empirical Bayesian Kriging is an interpolation method that accounts for the error in estimating the underlying semivariogram through repeated simulations.
Usage

This kriging method can handle moderately nonstationary input data.
Only Standard Circular and Smooth Circular Search neighborhoods are allowed for this interpolation method.
A Smooth Circular Search neighborhood will substantially increase the execution time.
The larger the Maximum number of points in each local model and Local model overlap factor values, the longer the execution time. Applying a Data transformation will also significantly increase execution time.
Syntax
Parameter  Explanation  Data Type 
in_features 
The input point features containing the zvalues to be interpolated.  Feature Layer 
z_field 
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 zvalues or mvalues.  Field 
out_ga_layer (Optional) 
The geostatistical layer produced. This layer is required output only if no output raster is requested.  Geostatistical Layer 
out_raster (Optional) 
The output raster. This raster is required output only if no output geostatistical layer is requested.  Raster Dataset 
cell_size (Optional) 
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 
transformation_type (Optional) 
Type of transformation to be applied to the input data.
 String 
max_local_points (Optional) 
The input data will automatically be divided into groups that do not have more than this number of points.  Long 
overlap_factor (Optional) 
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.  Double 
number_semivariograms (Optional) 
The number of simulated semivariograms.  Long 
search_neighborhood (Optional) 
Defines which surrounding points will be used to control the output. Standard is the default. This is a Search Neighborhood class SearchNeighborhoodStandardCircular and SearchNeighborhoodSmoothCircular. StandardCircular
SmoothCircular
 Geostatistical Search Neighborhood 
output_type (Optional) 
Surface type to store the interpolation results.
 String 
quantile_value (Optional) 
The quantile value for which the output raster will be generated.  Double 
threshold_type (Optional) 
Determines whether the probability values exceed the threshold value or not.
 String 
probability_threshold (Optional) 
The probability threshold value. If left empty, the median of the input data will be used.  Double 
Code Sample
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", "", "", "")
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
arcpy.CheckOutExtension("GeoStats")
# Execute EmpiricalBayesianKriging
arcpy.EmpiricalBayesianKriging_ga(inPointFeatures, zField, outLayer, outRaster,
cellSize, transformation, maxLocalPoints, overlapFactor, numberSemivariograms,
searchNeighbourhood, outputType, quantileValue, thresholdType, probabilityThreshold)