The Horvitz-Thompson Theorem as a Unifying Perspective for Probability Sampling: With Examples from Natural Resource Sampling

Abstract

Courses in sampling often lack a coherent structure because many related sampling designs, estimators, variances, and variance estimators are presented as separate cases. The Horvitz-Thompson theorem offers a needed integrating perspective for teaching the methods and fundamental concepts of probability sampling. Development of basic concepts in sampling via this approach provides the student with tools to solve more complicated problems, and helps to avoid some common stumbling blocks of beginning students. Examples from natural resource sampling are provided to illustrate applications and insight gained from this approach.

Key Words:

• Bitterlich sampling
• Environmental sampling
• Inclusion probability
• Systematic sampling
• Variable probability sampling