NMAK15022U Stereology

Volume 2015/2016
Education

MSc Programme in Statistics
 

Content

Stereology is  the estimation of geometrical quantities such as volume, area or length using lower dimensional samples of the object. The course will contain:

  • Integral geometry: Crofton's formula, parametrisation, uniform measures.
  • Fixed and isotropic, uniformly random probes (points, lines and planes).
  • Statistical formulations of stereology: Design-based and model-based approach.
  • Estimation in uniform designs: Systematic random sampling and systematic subsampling for area and volume. Length and surface area estimation
  • Estimation in local designs
  • Ratio estimation
  • Variance comparison of estimators. Asymptotic results.
  • Simulation of stereological estimators in R.
Learning Outcome

Knowledge:

Basic knowledge of the topics covered by the course: Crofton's formula, uniform measures, uniformly random probes, statistical formulations of stereology, estimation in uniform and local designs, ratio estimation, variance comparison, simulation of estimators.

Skill:

  • Use Crofton's formula to construct invariant measures on probes
  • Show that a given stereological estimator is central
  • Use Crofton's formula and uniform measures to derive new stereological estimators
  • Use simulation to compare specific estimators
  • Apply the estimation procedures to concrete examples

 

Competence:

  • Explain the connection between uniform measures and stereological estimators
  • Explain the difference between the design-based and the model-based approach to stereology
  • Discuss the difference between uniform and local designs
  • Compare estimators using asymptotic results
  • Explain systematic sampling estimators compared with other estimators.
  • Discuss the difficulties of estimating curves and surface areas compared with the estimation of area and volume

Lecture notes and selected parts of suitable monographs

Measures and integrals (MI) or equivalent
4 hours of lectures and 4 hours of exercises per week for 7 weeks. The second assignment will be in week 8.
  • Category
  • Hours
  • Exam
  • 40
  • Lectures
  • 28
  • Preparation
  • 112
  • Theory exercises
  • 28
  • Total
  • 208
Credit
7,5 ECTS
Type of assessment
Continuous assessment
There will be given 2 assignments. The first will count 40% and the second will count 60% towards the final grade.
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner
Re-exam

30 minutes oral examination with 30 minutes of preparation during which all aids are allowed.

Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.