MATU9MB - Statistical Inference

SCQF Level: 10
Availability: Autumn, Advanced module
Course Prerequisite: MATU9M2
Credit Value: 20 (1 module)

Aims

The course will provide a detailed introduction to the basic ideas of statistical inference using the likelihood approach. In particular, the theoretical basis of interval estimation and significance testing will be covered in some detail. Any necessary probability results will be introduced as required. A wide variety of applications will be used to motivate the concepts and to develop the practical skills of the students.

Learning Outcomes

Students should be able to identify appropriate probability models for specified situations, derive probability and moment generating functions, derive the maximum likelihood function, score function and information function, derive the likelihood ratio test statistic and implement these techniques to perform tests and calculate appropriate interval estimates for a wide range of real life situations.

Content

Revision of Probability. Likelihood Functions. Construction of interval and region estimates in one-parameter and multi-parameter situations. Approximate Inference. Generalised Likelihood Ratio Test and its Asymptotic version. Applications illustrating inferences within the context of One and Two samples and Categorical Data.

Transferable Skills

The ability to formulate problems in statistical terms and to present, analyse and interpret data with the use of Minitab.

Bibliography

G. KALBFLEISCH, "Probability and Statistical Inference Vols. I and II", S 76 KAL (RBR)

Teaching Format

There will be three one-hour lectures and one 1.5 hour practical per week.

Assessment

1/3 coursework (2 practical projects) and 2/3 examination.

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