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## ECM3728 - Statistical Inference (2015)

MODULE TITLE | Statistical Inference | CREDIT VALUE | 15 |
---|---|---|---|

MODULE CODE | ECM3728 | MODULE CONVENER | Dr Christopher Ferro (Coordinator) |

DURATION: TERM | 1 | 2 | 3 |
---|---|---|---|

DURATION: WEEKS | 0 | 11 weeks | 0 |

Number of Students Taking Module (anticipated) | 44 |
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Statistical models help us to describe and predict the real world, and are used in sectors as diverse as finance, insurance, economics, marketing, pharmaceuticals, sport, environment and government to name only a few. Statistical inference is the way we use data and other information to learn about and apply our models. This module introduces you to some of the main approaches to statistical inference and explains their associated procedures. The module establishes key theoretical concepts and results alongside explanations of their practical purpose and application. We will use simple computer simulations to illustrate basic concepts and as a tool for comparing procedures. You will gain practical experience with the methods through a series of worked examples and exercises.

Prerequisite module: ECM2709 or equivalent

This module aims to help you to develop a thorough understanding of the foundations of statistical theory from both frequentist and Bayesian perspectives, including the use of resampling. It also aims to help you to learn the concepts and mathematics that underlie this theory, and to apply the theory to a range of probability models.

.

On successful completion of this module, **you should be able to:**

**Module Specific Skills and Knowledge:**

1 demonstrate an understanding of the purpose of statistical inference, different approaches to statistical inference, and the key theoretical results and inferential procedures associated with these approaches;

2 apply these procedures to draw inferences about parametric statistical models, and compare different procedures critically.

**Discipline Specific Skills and Knowledge:**

3 demonstrate an understanding of the ways in which statistical inferential procedures and their performances may differ;

4 demonstrate an understanding of inferential concepts integral to statistical science;

5 progress to study a wider range of statistical inferential approaches in more detail.

**Personal and Key Transferable/ Employment Skills and Knowledge:**

6 demonstrate an understanding of key mathematical arguments, statistical concepts and practical issues important for advanced study, application and development of statistical science;

7 use the statistical programming environment 'R' to implement generic inferential procedures and to conduct simulation studies.

1. Frequentist Inference. The principles and methods of frequentist inference are explained. These include point estimation, consistency, efficiency and the Cramer-Rao bound; hypothesis testing, the Neyman-Pearson Theorem and uniformly most powerful tests; and confidence sets and their construction from hypothesis tests.

2. Likelihood Inference. Inferential approaches based on the likelihood are introduced. These include maximum likelihood estimators and their asymptotic properties, likelihood-based hypothesis tests and confidence sets, likelihoods for non-iid models, and pseudo likelihoods.

3. Resampling. Inferential approaches based on resampling are introduced. These include Monte Carlo and bootstrap tests, jackknife and bootstrap estimates of bias and variance, and bootstrap confidence sets.

4. Bayesian Inference. The principles of Bayesian inference are explained and contrasted with those of frequentist inference. This includes prior and posterior distributions, Bayes' Theorem, point summaries, credible sets, Bayes factors and predictive distributions.

Scheduled Learning & Teaching Activities | 33.00 | Guided Independent Study | 117.00 | Placement / Study Abroad |
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Category | Hours of study time | Description |

Scheduled learning and teaching activities | 33 | Lectures/example classes |

Guided independent study | 33 | Study of lecture notes |

Guided independent study | 44 | Attempting un-assessed and formative exercises |

Guided independent study | 25 | Revision |

Guided independent study | 15 | Assessment |

Form of Assessment | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
---|---|---|---|

Coursework - set assessment questions | 11 hours (1 hour each week) | All | Written feedback on script and oral feedback in tutorial and office hour |

Coursework | 20 | Written Exams | 80 | Practical Exams |
---|

Form of Assessment | % of Credit | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
---|---|---|---|---|

Written exam – closed book | 80 | 2 hours | 1-6 | Oral feedback at request from student |

Coursework – set assessment questions | 20 | 15 hours | All | Written feedback on script and oral feedback in office hour |

Original Form of Assessment | Form of Re-assessment | ILOs Re-assessed | Time Scale for Re-reassessment |
---|---|---|---|

All above | Written exam (100%) | All | August Ref/Def period |

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE – http://vle.exeter.ac.uk

Reading list for this module:

Type | Author | Title | Edition | Publisher | Year | ISBN | Search |
---|---|---|---|---|---|---|---|

Set | Garthwaite, Ph; Jolliffe, IT; Jones, B | Statistical Inference | 2nd | Oxford University Press | 2002 | 978-0198572268 | [Library] |

Extended | Azzalini, A | Statistical Inference - Based on the Likelihood | Chapman and Hall | 1996 | 978-0412606502 | [Library] | |

Extended | Barnett, V | Comparative Statistical Inference | 3rd | Wiley | 1999 | 978-0471976431 | [Library] |

Extended | Cox, D.R.; Hinkley, D.V. | Theoretical Statistics | Chapman and Hall | 1974 | 978-0412161605 | [Library] | |

Extended | Davison, A.C.; Hinkley, D.V. | Bootstrap Methods and their Application | Cambridge University Press | 1997 | 978-0521574716 | [Library] | |

Extended | Efron, B; Tibshirani, R.J. | Introduction to the Bootstrap | Chapman and Hall/CRC | 1994 | 978-0412042317 | [Library] | |

Extended | Pawitan Y | In All Likelihood: Statistical Modelling and Inference Using Likelihood | Oxford University Press | 2001 | 978-0198507659 | [Library] | |

Extended | Silvey, S.D. | Statistical Inference | Chapman and Hall | 1975 | 978-0412138201 | [Library] |

CREDIT VALUE | 15 | ECTS VALUE | 7.5 |
---|---|---|---|

PRE-REQUISITE MODULES | ECM2709 |
---|---|

CO-REQUISITE MODULES |

NQF LEVEL (FHEQ) | 6 | AVAILABLE AS DISTANCE LEARNING | No |
---|---|---|---|

ORIGIN DATE | Friday 09 January 2015 | LAST REVISION DATE | Friday 09 January 2015 |

KEY WORDS SEARCH | Statistics; mathematics; probability; data; analysis; modelling; inference. |
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