| CODE | SOR3243 | ||||||||||||
| TITLE | Bayesian Statistics | ||||||||||||
| UM LEVEL | 03 - Years 2, 3, 4 in Modular Undergraduate Course | ||||||||||||
| EQF/MQF LEVEL | 6 | ||||||||||||
| ECTS CREDITS | 4 | ||||||||||||
| DEPARTMENT | Statistics and Operations Research | ||||||||||||
| DESCRIPTION | Topics covered in this study-unit: 1. Mathematical Foundations of Bayesian Statistics 2. Prior Distributions: Types and properties of priors with reference to elicitation 3. Bayesian Decision theory 4. Bayesian Point Estimation 5. Hypothesis Testing through the posterior distribution 6. Bayesian Modelling : the theoretical , practical and computational platforms 7. Hierarchical Bayesian Models. Study-unit Aims: The aim of this unit is to provide a good grasp of the logic behind Bayesian statistical inference, i.e. the use of probability models to quantify uncertainty in statistical conclusions, and acquire skills to perform practical Bayesian analysis. Learning Outcomes: 1. Knowledge & Understanding By the end of the study-unit, students will be able to: - Explain the mathematical foundations of Bayesian inference, including the role of probability models, conditional probability, likelihood functions, and Bayes’ theorem in quantifying uncertainty; - Distinguish between different classes of prior distributions, describe their properties, and evaluate their suitability in applied contexts, including elicitation from expert knowledge; - Describe the principles of Bayesian decision theory, including loss functions, risk, admissibility, and the connection between decisions and posterior distributions; - Interpret posterior distributions for point estimation, interval estimation, and hypothesis testing, and articulate how Bayesian conclusions differ conceptually from frequentist ones; - Explain the structure and rationale of Bayesian models, including hierarchical and multilevel formulations, and identify the assumptions required for their validity; - Evaluate model fit and performance using Bayesian diagnostics, including posterior predictive checks, convergence diagnostics, and sensitivity to prior assumptions. 2. Skills By the end of the study-unit the student will be able to: - Conduct statistical analysis using Bayesian statistical Techniques; - Formulate model equations within the Bayesian paradigm and estimate corresponding statistical posterior distributions and performance diagnostics. Main Text/s and any supplementary readings: - Congdon P.D. (2020). Bayesian Hierarchical Models With Applications using R. Second edition. Taylor and Francis Group,LLC. - Lee, P.M (1997). Bayesian statistics: An introduction. Second edition. John Wiley and sons Inc. New York, NY. - Ghosh, J.K, Delampady M. and Samata, T. (2006). An Introduction to Bayesian Analysis: Theory and Methods. Springer Text in Statistics, USA. - Press, S. J. (2003). Subjective and Objective Bayesian statistics: Principals, Models and Applications. Second Edition, John Wiley and sons Inc. New York, NY. - Gelman , A. , Carlin J.B. Stein, H.S., Rubin D.B., (2004). Bayesian data analysis. Second Edition. Chapman and Hall/CRC, New York, NY. - Robert, C.P. (207) The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation. Springer Science & Business Media. - Richard McElreath (2016). Statistical Rethinking: A Bayesian Course with Examples in R and Stan. - Vladimir P. Savchuk & Chris P. Tsokos (2011) Bayesian Theory and Methods with Applications. Springer Science & Business Media. - Von Der Linden W., Dose V. and Von Toussant U. (2014). Bayesian Probability Theory Applications in the Physical Sciences. Cambridge University Press, Cambridge, United Kingdom. |
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| ADDITIONAL NOTES | Pre-Requisite Study-units: SOR1110, SOR2221 Co-Requisite Study-unit: SOR3500 |
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| STUDY-UNIT TYPE | Lecture and Tutorial | ||||||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Monique Borg Inguanez |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2026/7. It may be subject to change in subsequent years. |
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