MS2S25 - Advanced Probability and Statistics 01 Sep 2021 - 31 Aug 2027 | Version 1

Associated Module Information

Module Code: MS2S25
Module Title: Advanced Probability and Statistics
Faculty: Faculty of Computing, Engineering and Science
Faculty Group: Computing and Mathematical Sciences
Faculty Sub Group: Mathematical Sciences
Module Leader: Nicholas Andrews, Ian Fitzell
Module Team: Rebecca Peters, Ieuan Griffiths
First Intended Intake: SEP 2021 Final Year of Intake: 2024
Date Closed:
Credit Value: 20 Credit Level: 5
Language: English
Percentage of Module Taught in Welsh: 0
Equivalent Module:
HECOS codes:
HECOS Code Weighting:

Document Version Information

Version 1
Valid From 01 Sep 2021
Valid To 31 Aug 2027

Module Aims

To provide students with an understanding of advanced topics in probability and statistical inference.

To provide students with an understanding of using software for analysing data using advance probabilistic and statistical techniques.

Content Summary

Correlation and Regression:

Parametric and Non-Parametric methods, Bivariate Correlation, Multivariate Linear Regression, Residuals.

Analysis of Variance (ANOVA):

One-Way Analysis of Variance, Assumptions, Post – Hoc comparisons, non-parametric methods.

Cluster Analysis:

Measures of Distance, Hierarchical clustering – Agglomerative and Divisive, Non-hierarchical – k-means clustering, Dendrograms, Cubic Clustering Criterion, Pseudo F-Statistic, Pseudo t squared statistic.

Principal Component Analysis & Factor Analysis:

Dimensionality Reduction, Empirical Covariance Matrix, Eigenvalues and Eigenvectors and the PCA Algorithm, Factor Loadings, Kaisers Rule, Scree Plots, Rotation, Component Naming, Latent Variables, exploratory factor analysis, communalities.

Stochastic Processes:

Generalities on Stochastic Processes, Bernoulli Process, Poisson Process, Markov Chains.

Introduction to Time Series:

Generalities on Time Series Analysis, Classical Model, Trend and Seasonal Component, MA(q) model, AR(p) model, ARMA(p,q) model, ARIMA(p,d,q) model. Applications with real word data and models implementation using statistical software.

Learning and Teaching Methods

Activity Type Hours
Lecture 10
Practical classes and workshops 10
Supervised time in studio/workshop 6
Work based learning 74
Directed Study 28
Active/Simulation Based 72
Total Hours Selected 200

Learning Outcomes

# Learning Outcome
LO1 Understand the theory of probability and statistical inference
LO2 Select and apply the theory of probability and statistical inference to model complex situations.

Module Requisites

N/A

Assessment Criteria

Assessment Category Assessment Type Description Duration Word Count Weight (%) Best of? Pass Mark
Portfolio Portfolio 1 Portfolio 0 5000 100 No 40

Assessment Matrix

Assessment Type Learning Outcomes
LO1 LO2
Portfolio 1 ✔ ✔

Reading List

Berger, R. L., & Casella, G. (2008). Statistical Inference. Springer.

Brockwell, P. J., & Davis, R. A. (2016). Introduction to Time Series and Forecasting 3rd Edition. Springer.

Chan, K., & Cryer, J. D. (2020). Time Series Analysis 2nd Edition. Springer.

Wasserman, L. A. (2004). All of Statistics. Springer.