# Mathematics

## MTH2006 - Statistical Modelling and Inference (2018)

MODULE TITLE CREDIT VALUE Statistical Modelling and Inference 30 MTH2006 Dr Christopher Ferro (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 11 0
 Number of Students Taking Module (anticipated) 98
DESCRIPTION - summary of the module content

Statistical modelling lies at the heart of modern data analysis, helping us to describe and predict the real world. Statistical inference is the way that we use data and other information to learn about and apply statistical models. In this module, you will learn the theory underpinning modern statistical methods and apply these using statistical software to analyse and draw conclusions from a range of real-world data sets.

Prerequisite module: MTH1004 or equivalent

AIMS - intentions of the module

This module aims to develop understanding and competence in statistical modelling by introducing you to the Normal linear model from a modern perspective. It will provide you with the ability to formulate and apply these models in a range of practical settings, to carry out associated inference appreciating how this relates to the general likelihood inferential framework, and to perform appropriate model selection and model checking procedures. Use will be made of a suitable statistical computer language for practical work.

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 knowledge and understanding of inferential procedures, including point estimation, interval estimation and hypothesis testing;
2 apply these inferential procedures to draw correct inferences from data;
3 derive properties of basic inferential procedures;
4 formulate simple and multiple regression models and analyse their properties, including polynomial regression and models which involve categorical explanatory variables (i.e. factors) and understand how the latter relate to classical analysis of variance techniques;
5 demonstrate an awareness of the range of practical situations where it is, and is not, appropriate to employ Normal linear models;
6 demonstrate understanding of the theory and practice of estimation and inference for the Normal linear model and be able to apply this to fit models and carry out model selection and checking procedures in a range of practical situations;
7 carry out data analysis using multiple regression and related models in conjunction with a suitable computer language.
Discipline Specific Skills and Knowledge:
8 demonstrate understanding and appreciation of the mathematical modelling of stochastic phenomena and its usefulness;
9 demonstrate sufficient knowledge of fundamental ideas central to modern model-based statistics which are necessary to be able to progress to, and succeed in, further studies in statistical inference, statistical modelling of data and of stochastic modelling more generally.
Personal and Key Transferable/ Employment Skills and  Knowledge:
10 demonstrate general data analysis skills and communicate associated reasoning and interpretations effectively in writing;
11 use relevant computer software competently;
12 demonstrate appropriate use of learning resources;
13 demonstrate self management and time management skills.

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

-          revision of probability and statistical modelling;

-          maximum likelihood estimators and their asymptotic distribution;

-          properties of point estimators, including bias, standard error, mean squared error and consistency;

-          confidence intervals;

-          hypothesis tests, including z-tests and t-tests;

-          Monte Carlo simulation;

-          introduction to statistical modelling of relationships between variables

-          the multivariate Normal distribution: linear combinations of Normal variates, conditional distributions;

-          response and explanatory variables;

-          continuous and categorical data and associated considerations;

-          basic ideas of the Normal linear model and of associated concepts of model fitting, fitted values, residuals and goodness of fit;

-          model identification: descriptive/exploratory data analysis of relationships between variables;

-          summary measures of correlation and association, graphical techniques;

-          scatterplots, grouped box plots, scatterplot matrices, scatter plot smoothing;

-          the linear model for a single explanatory variable: simple regression;

-          model formulation, equivalence of maximum likelihood to least squares, point and interval parameter estimation and hypothesis testing (t-test), prediction from simple regression;

-          assessment of model fit, sum-of-squares breakdown, goodness of fit (R-squared and F-test), residual analysis,and influential observations;

-          the linear model for multiple continuous explanatory variables multiple regression;

-          model formulation in matrix notation, point and interval parameter estimation and hypothesis testing (partial t-tests), prediction from multiple regression, multicollinearity, assessment of model fit, sum-of-squares breakdown, goodness of fit (R-squared and F-test), residual analysis,and influential observations;

-          special cases of multiple regression: polynomial regression;

-          regression models with categorical explanatory variables: factors and auxiliary/indicator variables, ANOVA and ANCOVA;

-          model selection in regression: comparison of models, variable selection and model choice including stepwise procedures

-          going beyond the linear model transformation of variables, variance-stabilising transformation, Box-Cox transformation, weighted regression, robust regression;

-          approaches for dealing with missing data.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study Placement / Study Abroad 70 230 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled learning and teaching activities 48 Lectures including examples classes and 4 guest real-world application lectures Scheduled learning and teaching activities 11 Practicals in a computer lab Scheduled learning and teaching activities 11 Tutorials Guided independent study 230 Private study

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
Example sheets 5 x 10 hours 1-10 Oral feedback in weekly tutorial classes

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams Practical Exams 40 60 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – closed book 60 2 hours 1-10 Via SRS
Coursework 1 20 3000 words or equivalent 1-3 Written feedback on script and oral feedback in office hour
Coursework 2 20 3000 words or equivalent 4-8 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