kriging: an introduction to concepts and applications...empirical bayesian kriging...
TRANSCRIPT
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Kriging: An Introduction to
Concepts and ApplicationsEric Krause
Konstantin Krivoruchko
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Sessions of note…
Tuesday
• Kriging: An Introduction to Concepts and Applications (10:00-11:00 SDCC Rm02)
• ArcGIS for Geostatistical Analyst: An Introduction (1:00-2:00 SDCC Rm30A)
• Empirical Bayesian Kriging and EBK Regression Prediction in ArcGIS (2:30-3:15 SDCC Demo Theater 12)
• ArcGIS for Geostatistical Analyst: An Introduction (4:00-5:00 SDCC Rm30A)
Wednesday
Thursday
• Interpolating Surfaces in ArcGIS (10:00-11:00 SDCC Rm30C)
• Surface Interpolation in ArcGIS (11:15-12:00 SDCC Demo Theater 10)
• Kriging: An Introduction to Concepts and Applications (4:00-5:00 SDCC Rm08)
• Polygon-to-Polygon Predictions Using Areal Interpolation (11:15-12:00 SDCC Demo Theater 10)
• Interpolating Surfaces in ArcGIS (4:00-5:00 SDCC Rm31A)
2
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Geostatistical Analyst Resourceshttp://esriurl.com/GeostatGetStarted
• GeoNet – community.esri.com
- Blogs
- Free textbook and datasets
- Spatial Statistical Analysis For GIS Users
- Lots of discussions and Q&A
• Learn GIS – learn.arcgis.com
- Model Water Quality Using Interpolation
- Analyze Urban Heat Using Kriging
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Outline
• Introduction to interpolation
• Introduction to kriging
• Validating interpolation results
• Empirical Bayesian Kriging and EBK Regression Prediction
• Areal Interpolation
• Questions
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What is interpolation?
• Predict values at unknown locations using values at measured locations
• Many interpolation methods: kriging, IDW, LPI, etc
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What is autocorrelation?
Tobler’s first law of geography:
"Everything is related to everything else, but near things are more related than distant things."
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Semivariogram
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What is kriging?
• Kriging is the optimal interpolation method if the data meets certain
conditions.
• What are these conditions?
- Normally distributed
- Stationary
- No trends
• How do I check these conditions?
- Exploratory Analysis and charting
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What is an “optimal” interpolator?
• Estimates the true value, on average
• Lowest expected prediction error
• Able to use extra information, such as covariates
• Can be generalized to polygons (Areal interpolation, Geostatistical
simulations)
• Can estimate quantiles to test best/worst case scenarios
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Kriging workflow
1. Explore the data – check kriging assumptions
2. Configure options: trend removal, transformations, etc
3. Estimate a semivariogram model
4. Validate the results
5. Repeat steps 2-4 as necessary
6. Map the data for decision-making
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Exploring your data
1. Where is the data located?
2. What are the values of the data points?
3. How does the location of a point relate to its value?
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Does my data follow a normal distribution?
• Histogram chart
- Symmetric and bell-shaped
- Look for outliers
- Mean ≈ Median
• What can I do if my data is not
normally distributed?
- Apply a transformation
- Log, Box Cox, Arcsin, Normal Score
Transformation
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Skewed distributions and outliers
Skewed Distribution Outlier
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Normal Score Transformation
• Fits a smooth curve to the data
• Performs a quantile transformation to the
normal distribution
• Performs calculations with transformed
data, then transforms back at the end
• Simple kriging with normal score
transformation is default kriging method
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Assessing models using cross validation
• Used to determine the reliability of the model
- Iteratively discard each sample
- Use remaining points to estimate value at measured location
- Compare predicted versus measured value
• Calculates various statistics
- Root-mean-square : root of average squared deviation from true value
- Smaller is better
- Mean : the average of the deviations
- Should be close to zero
- Root-mean-square standardized : measures whether standard errors are
estimated correctly
- Should be close to one
- Average standard error : should be small and close to the root-mean-square
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Prediction Error of Predictions Probability Quantile
Kriging output surface types
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Demo
Kriging in the
Geostatistical
Wizard
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Empirical Bayesian Kriging
• Advantages
- Requires minimal interactive modeling, spatial relationships are modeled
automatically
- Usually more accurate, especially for small or nonstationary datasets
- Uses local models to capture small scale effects
- Doesn’t assume one model fits the entire data
- Standard errors of prediction are more accurate than other kriging methods
• Disadvantages
- Processing is slower than other kriging methods
- Limited customization
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How does EBK work?
1. Divide the data into subsets of a given size
- Controlled by “Subset Size” parameter
- Subsets can overlap, controlled by “Overlap Factor”
2. For each subset, estimate the semivariogram
3. Simulate data at input point locations and estimate new
semivariogram
4. Repeat step 3 many times. This results in a distribution of
semivariograms
5. Mix the local surfaces together to get the final surface.
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EBK Regression Prediction
• Allows you to use explanatory variable rasters to improve predictions
• Automatically extracts useful information from explanatory variables
• Uses Principle Components to handle multicollinearity
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Demo
EBK and EBK
Regression Prediction
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Areal Interpolation
• Predict data in a different geometry
- School zones to census tracts
• Estimate values for missing data
Obesity by school zone Obesity surface and
error surface
Obesity by census block
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Types of Areal Interpolation
• Average (Gaussian)
- Median age, average temperature
• Rate (Binomial)
- Cancer rates, obesity rates, percent of college graduates
• Event (Overdispersed Poisson)
- Animal counts, crimes
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Areal Interpolation Workflow
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Demo
Areal Interpolation
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