# Mathematics

## ECM3728 - Statistical Inference (2015)

MODULE TITLE CREDIT VALUE Statistical Inference 15 ECM3728 Dr Christopher Ferro (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 weeks 0
 Number of Students Taking Module (anticipated) 44
DESCRIPTION - summary of the module content

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

AIMS - intentions of the module

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.

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INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

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.

SYLLABUS PLAN - summary of the structure and academic content of the module

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.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study 33 117
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 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

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
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

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 20 80
DETAILS OF SUMMATIVE ASSESSMENT
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

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
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

RE-ASSESSMENT NOTES

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.

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE – http://vle.exeter.ac.uk

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 ECTS VALUE 15 7.5
PRE-REQUISITE MODULES ECM2709
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING 6 No Friday 09 January 2015 Friday 09 January 2015
KEY WORDS SEARCH Statistics; mathematics; probability; data; analysis; modelling; inference.