ST522: Computational Statistics
Comment
Entry requirements
Academic preconditions
Course introduction
intensive statistical methods as tools to investigate stochastic
phenomena and statistical procedures, and to perform statistical
inference, which is important in regard to conducting statistical
analysis based on computation and simulation.
The course builds on the
knowledge acquired in the courses calculus and mathematical statistics,
and gives an academic basis for studying the topics probability theory,
order statistics and extreme value statistics, that are part of the
degree.
In relation to the competence profile of the degree it is the explicit focus of the course to:
- Give the competence to handle model building and/or model calculations.
- Give skills to perform statistical analyses.
- Give theoretical knowledge about and practical experience with the application of methods and models in statistics.
Expected learning outcome
The learning objective of the course is that the student demonstrates the ability to:
- Reproduce
key theoretical results concerning elementary operations on random
variables and vectors, and to apply these to simple theoretical
assignments. - Reproduce and apply the fundamental theorems of random variate generation.
- Simulate variates and vectors from the most common distributions.
- Evaluate the quality of a random number generator.
- Apply the basic principles of variance reduction.
- Simulate complex systems and investigate their properties.
- Use simulation to approximate integrals.
- Use simulation to compute p-values and confidence intervals.
- Investigate properties of statistical procedures and estimators using simulation.
- Perform programming relevant to the content of the course in the statistical package used in the course.
- Identify and interpret relevant information in the output of the statistical package used in the course.
- Summarize the results of an analysis in a statistical report.
Content
The following main topics are contained in the course:
Random number generators, inversion method, rejection sampling, simulation from multivariate distributions, Markov Chain Monte Carlo methods, permutation and randomization tests, transformations, simulation of experiments and complex systems, Monte Carlo integration, simulation of stochastic processes, bootstrap methods, Bayesian models and methods, EM algorithm, nonparametric density estimation.
Literature
Examination regulations
Exam element a)
Timing
Tests
Projects
EKA
Assessment
Grading
Identification
Language
Examination aids
To be announced during the course
ECTS value
Additional information
The first part of the course is evaluated by projects.
The examination form for re-examination may be different from the exam form at the regular exam.
Exam element b)
Timing
Tests
Oral examination
EKA
Assessment
Grading
Identification
Language
Examination aids
To be announced during the course
ECTS value
Additional information
The second part of the course is evaluated at an oral exam. The oral exam is based on, but not limited to, projects made during the second half of the course.
The examination form for re-examination may be different from the exam form at the regular exam.
Indicative number of lessons
Teaching Method
In the intro phase a modified version of the classical lecture is employed, where the terms and concepts of the topic are presented, from theory as well as from examples based on actual data. In these hours there is room for questions and discussions. In the training phase the students work with data-based problems and discussion topics, related to the content of the previous lectures in the intro phase. In these hours there is a possibility of working specifically with selected difficult concepts. In the study phase the students work independently with problems and the understanding of the terms and concepts of the topic. Questions from the study phase can afterwards be presented in either the intro phase hours or the training phase hours.
Educational activities
Studying the course material and preparing the weekly exercises, individually or through group work.