SF2950 Applied Mathematical Statistics 7.5 credits
Tillämpad matematisk statistik
The overall purpose of the course is that the student should be well acquainted with statistical modelling and analysis of observd and experimental data and provide insight in statistical design of experiments, sampling methods and concepts in statistical quality control. During the course regression and variance analysis models are applied to real problems.
Educational level
Second cycleAcademic level (A-D)
DSubject area
Mathematics
Grade scale
A, B, C, D, E, FX, F
Course offerings
Spring 13 for programme students
Periods
Spring 13 P3 (7.5 credits)
Application code
60103Start date
2013 week: 2End date
2013 week: 11Language of instruction
EnglishCampus
KTH CampusNumber of lectures
Number of exercises
Tutoring time
DaytimeForm of study
NormalNumber of places
No limitationSchedule
Schedule (new window)Part of programme
- Degree Progr. in Engineering Physics, year 3, Optional
- Master (Two Years), Applied and Engineering Mathematics, year 1, Mandatory
- Master (Two Years), Computer Science, year 1, CSCG, Conditionally Elective
- Master (Two Years), Industrial Engineering and Management, year 1, FMIA, Mandatory
- Master (Two Years), Machine Learning, year 1, MAIA, Conditionally Elective
- Master (Two Years), Machine Learning, year 1, MAIB, Conditionally Elective
- Master (Two Years), Machine Learning, year 1, MAIC, Conditionally Elective
- Master (Two Years), Mathematics, year 1, MSFI, Recommended
- Master (Two Years), Mathematics, year 1, OS, Optional
Spring 14 for programme students
Periods
Spring 14 P3 (7.5 credits)
Application code
61020Start date
2014 week: 3End date
2014 week: 12Language of instruction
EnglishCampus
KTH CampusNumber of lectures
Number of exercises
Tutoring time
DaytimeForm of study
NormalNumber of places
No limitationSchedule
Schedule (new window)Part of programme
- Degree Progr. in Engineering Physics, year 3, Optional
- Degree Progr. in Industrial Engineering and Management, year 3, TMAI, Mandatory
- Master (Two Years), Applied and Computational Mathematics, year 1, Optional
- Master (Two Years), Applied and Computational Mathematics, year 1, FMIA, Conditionally Elective
- Master (Two Years), Applied and Computational Mathematics, year 1, MASA, Conditionally Elective
- Master (Two Years), Applied and Engineering Mathematics, year 1, Mandatory
- Master (Two Years), Machine Learning, year 1, MAIA, Conditionally Elective
- Master (Two Years), Machine Learning, year 1, MAIB, Conditionally Elective
- Master (Two Years), Machine Learning, year 1, MAIC, Conditionally Elective
- Master (Two Years), Mathematics, year 1, Optional
- Master (Two Years), Systems, Control and Robotics, year 1, Recommended
- Master (Two Years), Systems, Control and Robotics, year 2, Recommended
Spring 14 for programme students
Periods
Spring 14 P3 (7.5 credits)
Application code
60196Start date
2014 week: 4End date
2014 week: 12Language of instruction
EnglishCampus
KTH CampusNumber of lectures
Number of exercises
Tutoring time
DaytimeForm of study
NormalNumber of places
No limitationSchedule
Schedule (new window)Part of programme
Learning outcomes
To pass the course, the student should be able to do the following:
- analyse and model real data with statistical computer software
- analyse and apply the theory of the general linear model on real problems by estimating the parameters in the general model and quantify the uncertainty in those estimates and determine how this affect the conclusions when testing statistical hypothesis
- perform multiple regression analysis and determine the applicability of the model on a real problem
- Understand problems with observed data, such as simultaneity and sample selection bias, and know how to use instrumental variables.
- perform a one and two sided variance analysis and distinguish between systematic and random factor models in real modelling situations
- analyse and judge different choices of experimental plans, i.e., distinguish between completely randomised experiments, randomised blocks and Latin squares when planning and modelling experiments. Judge the applicability of randomised and stratified sampling.
- apply full and fractional 2k designs on concrete problems
- decide and apply nonparametric methods on real problems based on different modelling aspects
To receive the highest grade, the student should in addition be able to do the following:
- Combine all the concepts and methods mentioned above in order to solve more complex problems.
Course main content
Theory of the common linear model: Estimation, confidence intervals and hypothesis testing.
Regression analysis: Multiple regression analysis.
Modelling: selection bias, simultaneity, heteroskedasticity, multikollinearity and estimation methods for such problems. The LOGIT model.
Variance analysis: One, two and multi way variance analysis, hierarchical splitting. Systematical and stochastic components.
Experimental planning: Factor trial, totally randomised tests, randomised blocks, Latin squares totally and fractional 2k-experiments.
Sample theory: Simple random samples, stratified samples.
Statistical quality control: Differentiating and guided control.
Non parametric methods.
Eligibility
Previous knowledge is assumed equivalent to Mathematical Statistics SF1906 (5B1506) and Linear Algebra SF1604 (5B1109).
Literature
Material from the department.
Examination
- LAB1 - Laboratory Work, 1.5 credits, grade scale: P, F
- TEN1 - Examination, 6.0 credits, grade scale: A, B, C, D, E, FX, F
Requirements for final grade
Assignment (LAB1; 1,5 university credits), written exam (TEN1; 6 university credits).
Offered by
SCI/Mathematics
Examiner
Version
Course plan valid from:
Spring 11.
Examination information valid from:
Autumn 07.