Veidlapa Nr. M-3 (8)
Study Course Description
Computational Statistics
Course Code
SL_123
Branch of Science
Mathematics; Theory of probability and mathematical statistics
ECTS
3.00
Target Audience
Life Science
LQF
Level 7
Study Type And Form
Full-Time; Part-Time
Study Course Implementer
Course Supervisor
Ziad Taib
Structure Unit Manager
Andrejs Ivanovs
Structural Unit
Statistics Unit
Contacts
23 Kapselu street, 2nd floor, Riga, statistika@rsu.lv, +371 67060897
About Study Course
Objective
Computers are powerful tools in statistics enabling researchers to solve otherwise intractable problems and analyzing very large data sets using specific techniques. Statistical computing refers to the branch of statistics involving such techniques. This course gives an overview of the foundations and basic methods in statistical computing.
The objective of this course is to enable the students to:
• understand and apply standard methods for random number generation.
• understand principles and methods of stochastic simulation.
• apply different Monte Carlo methods.
• be familiar with software for statistical computing.
• implement statistical algorithms for a given problem.
Preliminary Knowledge
Knowledge of probability and statistics.
Learning Outcomes
Knowledge
1.After the course students will know the main topics covered by the course from a theoretical and practical point of view and will be able to: • classify statistical simulation-based computational methods. • identify and explain Monte-Carlo methods and Markov Chain Monte Carlo (MCMC) methods. • discuss resampling methods
Skills
1.• Reproduce random number generation. • Can independently use computation and programming skills as applicable to solving statistical problems. • Perform simulations using R. • Understand and apply resampling methods e.g. bootstrapping. • Capable of independent usage of theory and methods to carry out research activities and to write a paper, make presentation of results obtained based on simulation experiments.
Competences
1.• Evaluate the statistical computation framework for data analysis and when it can be beneficial, compared to the traditional statistical approach. • Perform statistical analyses in practice using simulation-based computational methods. • Determine the role of simulation and resampling, and the usage of these in complex problems. • Assess and interpret the results of simulation experiments.
Assessment
Individual work
|
Title
|
% from total grade
|
Grade
|
|---|---|---|
|
1.
Individual work |
-
|
-
|
|
• Individual work with the course material in preparation to all lectures according to plan.
• 4 computer projects – Individual work in group on agreed computer assignments. Students will perform computer experiments and analyse data by applying the methods presented throughout the course.
|
||
Examination
|
Title
|
% from total grade
|
Grade
|
|---|---|---|
|
1.
Examination |
-
|
-
|
|
Assessment on the 10-point scale according to the RSU Educational Order:
• Active participation in lectures, practical’s and exercises as well as computer projects – 20%.
• Handing out and presentation of reports on computer projects – 40%.
• Final written examination – 40%.
|
||
Study Course Theme Plan
FULL-TIME
Part 1
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Introduction and reminders: Probability and statistics reminders.
Introduction to random number generation methods.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
3
|
Topics
|
Computer project. R programming and random number generation.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Simulating statistical models: Multivariate normal distributions and Hierarchical models, Markov chains and Poisson processes.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
3
|
Topics
|
Computer project. Simulation of distributions and processes.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Monte Carlo methods: Exploring models via simulation – Monte Carlo estimates –Variance reduction methods – Applications to statistical inference.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
3
|
Topics
|
Computer project. Monte Carlo methods.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Convergence of Markov Chain Monte Carlo methods – Applications to Bayesian inference.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Resampling methods: Approximate Bayesian Computation – Empirical distributions – The bootstrap principle – Bootstrap estimation.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
3
|
Topics
|
Computer project. Resampling methods.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Continuous-time models: Time discretisation – Monte Carlo estimates – Examples and case studies.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Repetition and preparation for the exam.
|
Total ECTS (Creditpoints):
3.00
Contact hours:
26 Academic Hours
Final Examination:
Exam (Written)
PART-TIME
Part 1
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Introduction and reminders: Probability and statistics reminders.
Introduction to random number generation methods.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Computer project. R programming and random number generation.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Simulating statistical models: Multivariate normal distributions and Hierarchical models, Markov chains and Poisson processes.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Computer project. Simulation of distributions and processes.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Monte Carlo methods: Exploring models via simulation – Monte Carlo estimates –Variance reduction methods – Applications to statistical inference.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Computer project. Monte Carlo methods.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Convergence of Markov Chain Monte Carlo methods – Applications to Bayesian inference.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Resampling methods: Approximate Bayesian Computation – Empirical distributions – The bootstrap principle – Bootstrap estimation.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Computer project. Resampling methods.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Continuous-time models: Time discretisation – Monte Carlo estimates – Examples and case studies.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Repetition and preparation for the exam.
|
Total ECTS (Creditpoints):
3.00
Contact hours:
15 Academic Hours
Final Examination:
Exam (Written)
Bibliography
Required Reading
1.
Gelman, A., Carlin, J.B, Stern, H.S and Rubin, D.B. (2013). Bayesian Data Analysis 3rd ed. Chapman and Hall.
Additional Reading
1.
Voss, J. (2014). An introduction to statistical computing: a simulation-based approach. Wiley. Available from: https://ebookcentral.proquest.com/lib/rsub-ebooks/detail.action?docID=1355720
2.
Rizzo, M.L. (2008). Statistical computing with R /CRC, Boca Raton.
3.
Ripley, B.D. (2006). Stochastic simulation. Wiley.