| Module Code | STU34506 |
| Module Name | Modern Statistical Methods II |
| ECTS Weighting [1] | 5 ECTS |
| Semester taught | Semester 2 |
| Module Coordinator/s | Alessio Benavoli |
Module Learning Outcomes
Module Learning Outcomes
On successful completion of this module, students will have the ability to
LO1. Devise suitable simulation methods for generating random numbers from a given probability distribution.
LO2. Use the sampled random numbers to estimate quantities of interest or evaluate integrals.
LO3. Assess the quality of the generated sample via diagnostic tools.
LO4. Choose appropriate Monte Carlo sampling algorithms.
LO5. Apply stochastic simulation methods in practice.
LO6. Modify the methods for a specific application.
Module Content
Monte Carlo methods are stochastic simulation-based algorithms designed to compute approximated solutions to problems where exact solutions are intractable and take exponential time to compute. The scope of this module is to review fundamental aspects in Monte Carlo simulation.
Specific topics addressed in this module include:
• Random variable generation: transformation methods, accept-reject methods
• Monte Carlo integration and importance sampling
• Markov Chains Markov Chain Monte Carlo Methods, like Metropolis-Hastings and Gibbs sampler
• Sequential Monte Carlo Methods
• Theoretical aspects such as convergence and performance analysis
• Inference in Probabilistic programming through MCMC
It also gives an opportunity for students to apply these tools to practical problems in statistical learning, data science, machine learning, and other areas, using the R programming language.
Teaching and learning Methods
Live lecturers and QAs with accompanying lecture notes and handouts, available through Blackboard.
Blackboard discussion forums.
Assessment Details
| Assessment Component | Brief Description | Learning Outcomes Addressed | % of total | Week set | Week Due |
| Examination | 2 hours in-person exam | LO1, LO2, LO3, LO4, LO5, LO6 | 70% | N/A | N/A |
| Coursework | Project | LO1, LO2, LO3, LO4, LO5, LO6 | 30% | 8 | 11 |
Reassessment Details
In-person Examination (2 hours, 100%)
Contact Hours and Indicative Student Workload
| Contact Hours (scheduled hours per student over full module), broken down by: | 33 hours |
| Lecture | 29 |
| Tutorial or seminar | 4 |
| Independent study (outside scheduled contact hours), broken down by: | 82 hours |
| Preparation for classes and review of material (including preparation for examination, if applicable | 42 |
| completion of assessments (including examination, if applicable) | 40 |
| Total Hours | 115 hours |
Recommended Reading List
Robert, Christian, and George Casella. “Monte Carlo statistical methods”. Springer Science & Business Media, 2013.
Robert, Christian , and George Casella. “Introducing Monte Carlo methods with R”. Vol. 18. New York: Springer, 2010.
Module Pre-requisites
Prerequisite modules: STU23501, STU22005
Other/alternative non-module prerequisites: Basic R programming and knowledge of linear algebra will be useful.
Module Co-requisites
None