| CODE | SCI5020 | ||||||||
| TITLE | Principles of Statistical Inference | ||||||||
| UM LEVEL | 05 - Postgraduate Modular Diploma or Degree Course | ||||||||
| MQF LEVEL | 7 | ||||||||
| ECTS CREDITS | 5 | ||||||||
| DEPARTMENT | Faculty of Science | ||||||||
| DESCRIPTION | This study-unit will cover topics in both frequentist and Bayesian inference, including useful computational techniques in both areas. Topics that will be covered are: - Estimators, Properties of Estimators, Methods of Estimation: - Method of Moments, Least Squares, Maximum Likelihood, Likelihood Theory, Likelihood ratio test. - Prior distributions. Calculating Posterior distributions, Summarizing Posterior information. Credibility Intervals. - Hypothesis testing and model selection. - Computational skills such as Bootstrap, Expectation-Maximisation (EM) algorithm and Monte Carlo Markov Chains (MCMC). Study-Unit Aims: - To propose statistical inference as being essentially the main activity in statistical analysis with descriptive summarization, estimation and hypothesis testing as its three main branches; -To expose students to the mathematical underpinnings of the subject and the relevant tools for future use; - To provide a good grasp of the logic behind Bayesian statistical inference, that is, the use of probability models to quantify uncertainty in statistical conclusions, and acquire skills to perform practical Bayesian analysis; - To provide the computational skills to solve complex problems in statistical inference. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Distinguish between the nature of different schools of statistical inference within the context of selections from populations; - Demonstrate a critical understanding of different estimation methods; - Discuss any assumptions required by the studied models; - Apply the major results and models in practical applications. 2. Skills: By the end of the study-unit the student will be able to: - Use competently summarization methods to give compact statistical picture of various relevant situations; - Formulate statistical models to capture random features within specific systems; - Formulate properly statistical hypotheses and propose relative tests to analyze problems involving various degrees of randomness; - Formulate model equations within the Bayesian paradigm and estimate corresponding statistical posterior distributions and performance diagnostics; -Conduct Bayesian statistical analysis using statistical software such as R. Main Text/s and any supplementary readings: Main Texts: - Knight K. (1999) Mathematical Statistics, CRC [A] Parmigiani, G. and Inoue, L. Y. T., Decision Theory: Principles and Approaches, Wiley. - Ghosh, J.K, Delampady M. and Samata, T. (2006). An Introduction to Bayesian Analysis: Theory and Methods. Springer Text in Statistics, USA. - Robert, C.P. (2007) 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. -McLachlan G.J. and Krishnan T. (2008). The EM Algorithm and Extensions 2nd Edition. Wiley. - Shao J. and Tu D. (1995). The Jackknife and Bootstrap. Springer, New York. - Gamerman D. and Lopes H. F. (2006) Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition. Chapman & Hall/CRC Texts in Statistical Science. Supplementary Readings: - Roussas George G. (2013) A Course in Mathematical Statistics, Academic Press. - Congdon P.D. (2020). Bayesian Hierarchical Models With Applications using R. Second edition. Taylor and Francis Group, LLC. |
||||||||
| ADDITIONAL NOTES | Pre-Requisite Study-Unit: SOR1510 | ||||||||
| STUDY-UNIT TYPE | Lecture and Tutorial | ||||||||
| METHOD OF ASSESSMENT |
|
||||||||
| LECTURER/S | Monique Borg Inguanez Fiona Sammut David Paul Suda |
||||||||
|
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 2025/6. It may be subject to change in subsequent years. |
|||||||||