.
Computational Statistics
Study Course Description
Course Description Statuss:Approved
Course Description Version:4.00
Study Course Accepted:14.03.2024 11:37:51
| Study Course Information | |||||||||
| Course Code: | SL_123 | LQF level: | Level 7 | ||||||
| Credit Points: | 2.00 | ECTS: | 3.00 | ||||||
| Branch of Science: | Mathematics; Theory of Probability and Mathematical Statistics | Target Audience: | Life Science | ||||||
| Study Course Supervisor | |||||||||
| Course Supervisor: | Ziad Taib | ||||||||
| Study Course Implementer | |||||||||
| Structural Unit: | Statistics Unit | ||||||||
| The Head of Structural Unit: | |||||||||
| Contacts: | 23 Kapselu street, 2nd floor, Riga, statistika rsu[pnkts]lv, +371 67060897 | ||||||||
| Study Course Planning | |||||||||
| Full-Time - Semester No.1 | |||||||||
| Lectures (count) | 7 | Lecture Length (academic hours) | 2 | Total Contact Hours of Lectures | 14 | ||||
| Classes (count) | 4 | Class Length (academic hours) | 3 | Total Contact Hours of Classes | 12 | ||||
| Total Contact Hours | 26 | ||||||||
| Part-Time - Semester No.1 | |||||||||
| Lectures (count) | 7 | Lecture Length (academic hours) | 1 | Total Contact Hours of Lectures | 7 | ||||
| Classes (count) | 4 | Class Length (academic hours) | 2 | Total Contact Hours of Classes | 8 | ||||
| Total Contact Hours | 15 | ||||||||
| Study course description | |||||||||
| Preliminary Knowledge: | Knowledge of probability and statistics. | ||||||||
| 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. | ||||||||
| Topic Layout (Full-Time) | |||||||||
| No. | Topic | Type of Implementation | Number | Venue | |||||
| 1 | Introduction and reminders: Probability and statistics reminders. Introduction to random number generation methods. | Lectures | 1.00 | auditorium | |||||
| 2 | Computer project. R programming and random number generation. | Classes | 1.00 | computer room | |||||
| 3 | Simulating statistical models: Multivariate normal distributions and Hierarchical models, Markov chains and Poisson processes. | Lectures | 1.00 | auditorium | |||||
| 4 | Computer project. Simulation of distributions and processes. | Classes | 1.00 | computer room | |||||
| 5 | Monte Carlo methods: Exploring models via simulation – Monte Carlo estimates –Variance reduction methods – Applications to statistical inference. | Lectures | 1.00 | auditorium | |||||
| 6 | Computer project. Monte Carlo methods. | Classes | 1.00 | computer room | |||||
| 7 | Convergence of Markov Chain Monte Carlo methods – Applications to Bayesian inference. | Lectures | 1.00 | auditorium | |||||
| 8 | Resampling methods: Approximate Bayesian Computation – Empirical distributions – The bootstrap principle – Bootstrap estimation. | Lectures | 1.00 | auditorium | |||||
| 9 | Computer project. Resampling methods. | Classes | 1.00 | computer room | |||||
| 10 | Continuous-time models: Time discretisation – Monte Carlo estimates – Examples and case studies. | Lectures | 1.00 | auditorium | |||||
| 11 | Repetition and preparation for the exam. | Lectures | 1.00 | auditorium | |||||
| Topic Layout (Part-Time) | |||||||||
| No. | Topic | Type of Implementation | Number | Venue | |||||
| 1 | Introduction and reminders: Probability and statistics reminders. Introduction to random number generation methods. | Lectures | 1.00 | auditorium | |||||
| 2 | Computer project. R programming and random number generation. | Classes | 1.00 | computer room | |||||
| 3 | Simulating statistical models: Multivariate normal distributions and Hierarchical models, Markov chains and Poisson processes. | Lectures | 1.00 | auditorium | |||||
| 4 | Computer project. Simulation of distributions and processes. | Classes | 1.00 | computer room | |||||
| 5 | Monte Carlo methods: Exploring models via simulation – Monte Carlo estimates –Variance reduction methods – Applications to statistical inference. | Lectures | 1.00 | auditorium | |||||
| 6 | Computer project. Monte Carlo methods. | Classes | 1.00 | computer room | |||||
| 7 | Convergence of Markov Chain Monte Carlo methods – Applications to Bayesian inference. | Lectures | 1.00 | auditorium | |||||
| 8 | Resampling methods: Approximate Bayesian Computation – Empirical distributions – The bootstrap principle – Bootstrap estimation. | Lectures | 1.00 | auditorium | |||||
| 9 | Computer project. Resampling methods. | Classes | 1.00 | computer room | |||||
| 10 | Continuous-time models: Time discretisation – Monte Carlo estimates – Examples and case studies. | Lectures | 1.00 | auditorium | |||||
| 11 | Repetition and preparation for the exam. | Lectures | 1.00 | auditorium | |||||
| Assessment | |||||||||
| Unaided 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. | ||||||||
| Assessment Criteria: | 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%. | ||||||||
| Final Examination (Full-Time): | Exam (Written) | ||||||||
| Final Examination (Part-Time): | Exam (Written) | ||||||||
| Learning Outcomes | |||||||||
| Knowledge: | 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: | • 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. | ||||||||
| Competencies: | • 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. | ||||||||
| Bibliography | |||||||||
| No. | Reference | ||||||||
| 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.ac… | ||||||||
| 2 | Rizzo, M.L. (2008). Statistical computing with R /CRC, Boca Raton. | ||||||||
| 3 | Ripley, B.D. (2006). Stochastic simulation. Wiley. | ||||||||
