# STAT40820 Monte Carlo (online)

This module will discuss several computational methods that rely on repeated random sampling to approximate numerical quantities of interest. In particular, the methods here explored will concern strategies to simulate from probability distributions in order to numerically compute different estimates of interest and to carry out inferential statements. This course will make use of the free statistical software package R (www.r-project.org).

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Curricular information is subject to change

Learning Outcomes:

Knowledge and understanding of:
- Various random numbers generation methods (for both uniform and non-uniform random variables)
- Monte Carlo methods (Rejection method, Importance Sampling)
- Various Markov Chain Monte Carlo methods (Gibbs sampler, Metropolis-Hastings, diagnostic techniques)
- Advanced topics in Monte Carlo methods (Control Variates, Antithetic Variates, Simulated Annealing, Monte Carlo Hp tests)

Both theoretical and practical aspects of the different methods will be illustrated. Implementation of the methods discussed will be explored using the R programming language.

Student Effort Hours:
Student Effort Type Hours
Specified Learning Activities

24

Autonomous Student Learning

72

Online Learning

24

Total

120

Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based learning.
Requirements, Exclusions and Recommendations
Learning Requirements:

- Basic understanding of probability. For more details on the required level, see for example the content and learning outcomes of STAT20110 - Introduction to Probability;
- Familiarity with common statistical distributions e.g. Gaussian, Gamma, Beta, Exponential, etc. ;
- Basic knowledge of function optimization (mathematical optimization);
- Basic understanding of statistical inference and hypothesis testing. For more details on the required level, see for example the content and learning outcomes of STAT20100 - Inferential Statistics.

Learning Recommendations:

- Basic knowledge of Stochastic Processes;
- Basic knowledge of Bayesian Inference;
- Basic knowledge of R programming language.

Module Requisites and Incompatibles
Incompatibles:
STAT40400 - Monte Carlo Inference

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Continuous Assessment: Online assessments Throughout the Trimester n/a Alternative linear conversion grade scale 40% No

30

Examination: End of trimester written exam 2 hour End of Trimester Exam No Alternative linear conversion grade scale 40% No

70

Carry forward of passed components
No

Resit In Terminal Exam
Spring Yes - 2 Hour