Undergraduate Programme and Module Handbook 2024-2025

# Module MATH2711: Statistical Inference II

## Department: Mathematical Sciences

### MATH2711: Statistical Inference II

Type | Open | Level | 2 | Credits | 20 | Availability | Available in 2024/2025 | Module Cap | None. | Location | Durham |
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#### Prerequisites

- Calculus I (Maths Hons) (MATH1081) or Calculus I (MATH1061), Linear Algebra I (Maths Hons) (MATH1091) or Linear Algebra I (MATH1071), Probability I (MATH1597) and Statistics I (MATH1617)

#### Corequisites

- None

#### Excluded Combination of Modules

- None

#### Aims

- To introduce the main concepts underlying statistical inference and methods.
- To develop the statistical and mathematical foundations underlying classical statistical techniques, and develop the basis for the Bayesian approach to statistics
- To investigate and compare the frequentist and Bayesian approaches to statistical inference.

#### Content

- Frequentist inference for Normal data
- Likelihood methods, maximum likelihood, Fisher's information
- Likelihood ratio tests and optimal testing
- Goodness of fit and probability models
- Nonparametric methods
- Multivariate statistics and the multivariate Normal
- Statistical decision theory
- Bayesian methods, prior distributions and conjugacy
- Bayesian inference

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module students will: be able to solve a range of predictable and unpredictable problems in statistical inference.
- have an awareness of the abstract theoretical concepts underlying statistics to a level appropriate to Level 2.
- have a knowledge and understanding of fundamental theories of these subjects demonstrated through one or more of the following topic areas: statistical inference, frequentist and likelihood methods, Bayesian statistics.

Subject-specific Skills:

- Students will have the ability to undertake and defend the use of alternative mathematical skills in the following areas with minimal guidance: statistical modelling, statistical analysis of unseen data sets.
- Students will have enhanced mathematical skills in the following areas: Statistical computing with R.

Key Skills:

- Students will have basic mathematical skills in the following areas: problem solving, statistical modelling, data analysis, statistical computation.

#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

- Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
- Problem classes show how to solve example problems in an ideal way, revealing also the thought processes behind such solutions.
- Computer practicals consolidate the studied material, explore theoretical ideas in practice, enhance practical understanding, and develop practical data analysis skills.
- Tutorials provide active problem-solving engagement and immediate feedback to the learning process.
- Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
- Formative assessments provide feedback to guide students in the correct development of their knowledge and skills in preparation for the summative assessment.
- The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

#### Teaching Methods and Learning Hours

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 52 | Three in weeks: 1, 2, 4, 6, 8, 10, 11, 12, 14, 16, 18, 20; two in weeks 3, 5, 7, 9, 13, 15, 17, 19. | 1 hour | 52 | |

Tutorials | 10 | Weeks 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. | 1 hour | 10 | ■ |

Problem Classes | 8 | One in wks 3, 5, 7, 9, 13, 15, 17, 19. | 1 hour | 8 | |

Computer Practicals | 8 | Weeks 3, 5, 7, 9, 13, 15, 17 19. | 1 hour | 8 | ■ |

Preparation and reading | 122 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 100% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

Written Examination | 3 hours | 100% |

#### Formative Assessment:

• Weekly written or electronic assignments to be assessed and returned. • Other assignments are set for self-study and complete solutions are made available to students.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University