Module: Statistics II

Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title	Statistics II
Module Code	MS228
School	School of Mathematical Sciences
Module Co-ordinator	Semester 1: Vladimir Krylov Semester 2: Vladimir Krylov Autumn: Vladimir Krylov
Module Teachers	Vladimir Krylov
NFQ level	8	Credit Rating	7.5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Repeat examination

Description

MS228 aims to provide a strong foundation in the fundamental statistical method of regression modelling. Simple and multiple linear regression models will be presented. The fitting and interpretation of regression models will be explained and practical examples given. The linear model will be extended to model non normal data using generalised linear models (GLMs). The regression models will be applied to practical datasets using R. Students will also be introduced to Bayesian statistical methods and their use in credibility theory.

Learning Outcomes

1. Perform exploratory data analysis techniques on a sample of data.
2. Describe and interpret linear regression models and estimate the parameters of a simple linear regression model.
3. Describe and interpret generalised linear models (GLMs).
4. Fit linear and generalised linear models to datasets using R and apply appropriate model checks.
5. Understand the Bayesian approach to statistical modelling.
6. Apply the Bayesian and empirical Bayesian approaches to credibility theory.

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	30	Classes
Tutorial	10	Classes
Laboratory	10	Computer labs
Independent Study	138	Individual
Total Workload: 188

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Exploratory Data Analysis
Data visualisation – histograms, box plots, scatter plots, heatmaps. Use of R visualisation packages. Correlation measures. Introduction to Principal Components Analysis. Use of R to implement analysis techniques.

Linear Regression
Exploratory data analysis; correlation; least squares estimation; model fitting in R; goodness of fit measures; residual checking; predication; confidence intervals.

Multiple Linear Regression
Model definition; modelling fitting and checking in R.

Generalised Linear Models (GLM)
Exponential family - binomial, Poisson, exponential, gamma and normal; link function and canonical link function; deviance and scaled deviance; model fitting in R; Pearson Chi-square test and the Likelihood ratio test; model interpretation.

Bayesian Statistics
Bayes theorem; prior and posterior distributions; loss functions.

Credibility Theory
Credibility premium; Bayesian approach to credibility theory; empirical Bayes approach to credibility theory.

Assessment Breakdown
Continuous Assessment	30%	Examination Weight	70%

Type	Description	% of total	Assessment Date
Course Work Breakdown
Assignment	lab assignment	30%	n/a

Reassessment Requirement Type
Resit arrangements are explained by the following categories; 1 = A resit is available for all components of the module 2 = No resit is available for 100% continuous assessment module 3 = No resit is available for the continuous assessment component
This module is category 1

Indicative Reading List

Other Resources

None

Programme or List of Programmes

ACM	BSc in Actuarial Mathematics
BPM	BSc in Psychology with Mathematics
CAFM	Common Entry, Actuarial, Financial Maths
DS	BSc in Data Science
ECSA	Study Abroad (Engineering & Computing)
ECSAO	Study Abroad (Engineering & Computing)

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