### MAS3302 : Introduction to Statistical Inference

• Module Leader(s): Dr David Walshaw
• Owning School: Mathematics & Statistics
##### Semesters
 Semester 1 Credit Value: 10 ECTS Credits: 5.0

#### Aims

To develop a knowledge and understanding of basic ideas of statistical inference. To introduce the method of maximum likelihood as a general approach to estimation.

Module Summary

This module develops further the ideas of statistical inference for which the foundations were laid in MAS1341 and MAS1342 (or MAS2341 and MAS2342). Ideas of estimation and hypothesis tests will be reviewed. General properties of maximum likelihood estimators are explored. Many of the important properties apply asymptotically, that is in large samples, and this will be shown by simulation using R. The asymptotic properties allow the construction of approximate (large sample) hypothesis tests and confidence intervals, and this will be shown. In certain important cases, such as the Normal distribution, exact (small sample) results can be obtained and these give tests and confidence intervals for the means and variances of the relevant populations. In situations where no distributional results can be used, an alternative non-parametric approach will be demonstrated for one specific case. The use of the chi-squared, t and F distributions in this will be explained. Exact inference about proportions using the binomial distribution will also be explained.

#### Outline Of Syllabus

Review of single parameter likelihood inference. Parameter estimation: bias, consistency, mean square error. Sufficiency. Score and information. Asymptotic distribution of maximum likelihood estimator; verification by simulation. Method of moments as an alternative estimation technique. Hypothesis tests: power, effect of sample size. Neyman Pearson Lemma. Inference for one and two normal random samples (using chi-squared, t and F distributions, with definitions by functions of random variables); inference for one and two sample (binomial) proportions. Standard error, confidence intervals and hypothesis testing (Z tests and t-tests) based on asymptotic normality. The Mann Whitney test as a non-parametric alternative to the t-test. Small sample inference based on exact methods. Goodness of fit tests and the use of normal probability plots. Use of R.

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture61:006:00Problem classes
Guided Independent StudyAssessment preparation and completion111:0011:00Revision for unseen Exam
Guided Independent StudyAssessment preparation and completion11:301:30Unseen Exam
Guided Independent StudyAssessment preparation and completion16:006:00Revision for class test
Scheduled Learning And Teaching ActivitiesLecture221:0022:00Formal lectures
Guided Independent StudyAssessment preparation and completion11:001:00Class test
Guided Independent StudyAssessment preparation and completion44:0016:00Written assignments and CBAs
Scheduled Learning And Teaching ActivitiesPractical31:003:00N/A
Scheduled Learning And Teaching ActivitiesDrop-in/surgery61:006:00Drop-ins in the lecture room
Guided Independent StudyIndependent study41:004:00Assignment review
Guided Independent StudyIndependent study121:3021:30Studying, practising and gaining understanding of course material
Total100:00
##### Jointly Taught With
Code Title
MAS2302Introduction to Statistical Inference
##### Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the studentsâ€™ abilities at applying the theory to solving problems. Drop-ins are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. Practicals are used both for solution of problems and work requiring extensive computation and for simulation to give insight into the ideas/methods studied. Office hours provide an opportunity for more direct contact between individual students and the lecturer.

#### Assessment Methods

The format of resits will be determined by the Board of Examiners

##### Exams
Description Length Semester When Set Percentage Comment
Written Examination901A80unseen
##### Exam Pairings
Module Code Module Title Semester Comment
MAS2302Introduction to Statistical Inference1N/A
##### Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M10Written assignments and computer based assessments
Prob solv exercises1M10Coursework test
##### Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. Coursework assignments (approximately 4 assignments of approximately equal weight) and a coursework test (in class) allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; this is thus formative as well as summative assessment. The coursework assignments may be written assignments, computer based assessments or a combination of the two, and in the case of combined assessments the deadlines for the two parts will not necessarily be the same.