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Hybrid Inference

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    Shutterstock, Mila Supinskaya

NOVA PhD course of 5 ECTS, organised by Prof. Terje Gobakken, Norwegian University of Life Sciences.
Course dates and location: 27-31 May 2019, in Ås, Norway.

Nordic Forest Research (SNS)
Nordic Forest Research (SNS)
Nordic Forest Research (SNS)
This course is funded by NOVA and Nordic Forest Research (SNS).

Course Description
In sample surveys, there are two main inferential approaches: the design-based and model-based. The probability sampling theory is part of the former, regression analysis and econometrics provide estimators within the latter inferential mode. Hybrid inference was developed by Nordic scientists to satisfy needs in surveys of natural resources in which auxiliary data from remote sensing play an important role. The new hybrid inference combines properties of the design- and model-based approaches and accounts for uncertainties due to both design and model. The course will provide a general and practical view, as well as a deeper scientific understanding of the new hybrid inferential approach.

The course will focus on the hybrid inferential approach for surveying discrete and continuous natural populations in the presence of auxiliary data. It includes elements from sampling survey theory, such as general sampling concept for discrete and continuous populations, sampling with fixed area plots, relascope sampling, stratified sampling and cluster sampling; as well as elements from regression analysis, such as ordinary least squares regression, generalized least squares regression and maximum likelihood estimators.

Programme Outline

  • May 5-25: pre-campus assignment
  • May 26: arriving in Ås
  • Week May 27-31:
    • Monday:
      • Course introduction
      • Design-based inference
      • Two-stage sampling
      • Model-based inference
      • Generalized least squares (GLS) regression estimator
      • Maximum likelihood (ML) and restricted ML (REML) estimator
      • Hybrid inference
  • June 2 – 14: Home exam

Pre-/Post-Campus Assignments

  • Pre-campus assignment: reading
    · Chapters 4, 5, 7 and 8 in “Sampling Strategies for Natural Resources and the Environment” by Gregoire, Timothy G. & Harry T. Valentine.
    · Ståhl, Göran, Sören Holm, Timothy G. Gregoire, Terje Gobakken, Erik Næsset, and Ross Nelson. Model-based inference for biomass estimation in a LiDAR sample survey in Hedmark County, Norway. Canadian Journal of Forest Research 41, no. 1 (2011): 96-107.
  • Post-campus assignment: a home exam.

Learning Outcomes

  • Knowledge and understanding:
    • Understand the framework of natural resource surveys;
    • Understand the concept of hybrid inference;
    • Understand differences between design-based, model-based and hybrid inferential approaches;
    • Know important theory related to sampling and regression analysis;
  • Skills and abilities:
    • Describe and quantify errors in natural resources surveys within hybrid inferential approach;
    • Apply relevant sampling designs such as simple random sampling, stratified sampling or cluster sampling;
    • Perform regression analysis with OLS, GLS regression and ML estimators.
  • Competences:
    • Synthesize knowledge and skills to survey natural populations within hybrid inferential approach by means by means of auxiliary information.

Evaluation Elements
The grading for the course is “Pass” or “Fail” and will be based on the evaluation of the home exam.

Pedagogical Approach
The course includes lectures, data exercises, group work and a seminar. Lectures will be given by leading scientist from the Nordic countries and USA. In the end of the course, students will be given the home exam tasks, which should be seen as a repetition of previously given material.

Estimated Workload

  • 2 hours seminar
  • 20 hours lecture
  • 18 hours independent work in the class
  • 60 hours independent work on pre-course assignment
  • 50 hours independent work on home exam after the course

Prerequisite Knowledge
It is recommended that participants have a basic knowledge in regression analysis and statistics, e.g. acquired through participation in basic courses at Master level. Basic knowledge in linear algebra is expected but not mandatory. To follow the course, basic knowledge in R is not required but preferable.


Admission for NOVA courses is handled by the course organiser/ the NOVA member institution organising the course. Please see the links in the margin for more information.

Apply here


NOK2,500 for accomoodation for the whole course, plus NOK350/day for meals.

Published 13. December 2018 - 11:30 - Updated 29. March 2019 - 10:20