NMAK15022U Stereology
MSc Programme in Statistics
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.
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
- Category
- Hours
- Exam
- 40
- Lectures
- 28
- Preparation
- 112
- Theory exercises
- 28
- Total
- 208
As
an exchange, guest and credit student - click here!
Continuing Education - click here!
- Credit
- 7,5 ECTS
- Type of assessment
- Continuous assessmentThere 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.
Course information
- Language
- English
- Course code
- NMAK15022U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 3
- Schedule
- A
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Anders Rønn-Nielsen (9-6c7d797470777e70794b786c7f73397680396f76)
Phone: +45 35 32 07 17