F79MA - Statistical Models A

Course leader(s):

• Alistair Wallis (Edinburgh, September)
• Maheen Hasib (Dubai, September)
• Huei Ching Soo (Malaysia, September)

Syllabus

1. Parameter estimation (1.1 Notation and definitions, 1.2 The method of moments, 1.3 Interval estimation, 1.4 The method of pivots)

2. The likelihood function (2.1 Definition and example, 2.2 Point and interval estimation, 2.3 Invariance under transformations, 2.4 Likelihood principle and the factorisation theorem)

3. The Cramer-Rao Theorem (3.1 A lower bound for the variance of an unbiased estimator, 3.2 Attaining the Cramer-Rao lower bound, 3.3 Minimum variance unbiased estimators MVUEs, 3.4 Classic properties of MLEs, 3.5 Extension to multi-parameter models)

4. Statistical inference in practice (4.1 Practical sampling problems, 4.2 Case studies, 4.3 Computing exercises, 4.4 Project work and report writing)

5. Hypothesis testing (5.1 Revision of the classical approach, from the NP lemma to GLRT’s)

6. Introduction to Bayesian inference (6.1 Introduction and prior information, 6.2 Prior and posterior distributions, 6.3 Conjugate priors, 6.4 Bayesian estimation, 6.5 Choice of prior distribution, 6.6 Bayesian decision theory)

7. Credibility theory (7.1 Credibility estimators, 7.2 Bayesian and empirical Bayesian approaches, 7.3 The Bühlmann model)

Learning outcomes

By the end of the course, students should be able to do the following:

• apply the properties of good estimators within an industry standard context.
• demonstrate critical understanding of Cramer-Rao Lower Bound and Rao-Blackwell Theorem and their applications to appropriate problems.
• evaluate in-depth understanding of Maximum Likelihood Estimation (MLE) method and its application to simple and complicated problems.
• apply classical and Bayesian hypothesis to practical problems.
• analyse the results of credibility premiums.

Further details

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SCQF Level: 9

Credits: 15