Introducing Spatial Statistics

Lecture 14

Wayne Tai Lee

Learning Objectives

• Understand different types of spatial datasets
• Crash course on spatial statistics

Types of spatial data

Polygons

Lines

Points

Points example - weather station measurements

Photo credit from NOAA USHCN website

Line example - routes

Polyon Example - US Building Footprint

Thanks to Microsoft for the BuildingFootprint dataset!

Why are there different types of data?

We often talk about records being (X₁, X₂, X₃, …, X_p)

• What is the distance between X₁ and X₂ ?
• Now what if one is a line and the other is a point?
• Now what if both are polygons?

Quick note on data on Earth - projections

Image from YouTube

Practice!

Canvas/Files/Notebooks/introducing_spatial_stat.ipynb

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Libraries:

• sp, rgeos, rgdal (spatial data manipulation)
• fields (statistical packages)

Spatial Statistics - modeling

Spatial Statistics - modeling

• Our belief about the data at s₁ is influenced by our expectation at that location
• Deviations from the expectations is where the neighboring data points help us understand

Model - spatial data is a noisy observation of a surface

Kriging - the OLS of spatial modeling

Kriging formula explained

Kriging formula explained

Kriging formula explained

Kriging formula explained

Choices for kriging - what exactly are these values?

can be the great circle distance

Choices for kriging - mean is a vector

can be the great circle distance

Choices for kriging - covariance is a matrix

can be the great circle distance

Choices for kriging - distance is a matrix

can be the great circle distance