Data Analytics and AI MSc

Cover introductory topics in statistics and probability that could be applied to data analysis in a broad range of subjects.

Topics include:

• common univariate probability distributions
• joint and conditional distributions
• parameter estimation (for example via maximum likelihood)
• confidence intervals
• hypothesis testing
• statistical modelling

Consideration is given to issues in applied statistics such as data collection, design of experiments, and reporting statistical analysis.

Topics will be motivated by solving problems and case studies, with much emphasis given to simulating and analysing data using computer software to illustrate the methods.

For this module, you will carry out a substantial investigation on a topic at the frontiers of data analytics and AI. You’ll have a supervisor who will provide oversight and input to support you with this self-directed project.

You’ll agree on your topic with your supervisor, drawing on a range of topics that reflect the broad expertise of academic staff in both the School of Mathematical Sciences and Nottingham University Business School. Where appropriate, your project may also be inspired by and/or conducted in collaboration with one of our industrial partners, either within the University of Nottingham or as a placement at the partner’s site.

This module will introduce fundamental tools, techniques and skills required for data analytics roles in modern, data-rich and data-driven environments across diverse industries.

You will develop practical skills such data collection, cleaning and preprocessing, using industry-standard tools such as, Python, R and SQL. You will also learn about big data technologies, dealing with large databases alongside contemporary visualisation tools.

There will be an emphasis on hands-on experience with analytics workflows (such as version control) alongside the fundamental mathematical tools required to apply core statistical, probabilistic and machine learning concepts for data-driven decision making.

Furthermore, you will develop key soft skills, such as crafting clear and insightful reports, presenting data-driven findings effectively, and communicating complex analytics to both technical and non-technical audiences.

This module introduces fundamental statistical concepts and key descriptive modelling techniques in data science, while laying a foundation for the general programming skills required by any top modern business analyst (for example, Python/R).

A range of descriptive modelling concepts will be covered (such as feature engineering, clustering techniques, rule mining, topic modelling and dimensionality reduction) against a background of real world datasets (predominantly based on consumer data).

You will learn not only how to successfully implement foundational descriptive techniques, but also how to evaluate and communicate results in order to make them effective in actual business environments.

This module introduces the fundamental concepts and technologies that are used by modern international businesses to store, fuse, manipulate and visualise mass datasets. 

Key concepts include:

• core database and cloud technologies
• data acquisition and cleansing
• how to manipulate mass datasets (focusing on SQL, Hadoop)
• effective solutions to common data challenges (for example, missing data)
• handling geospatial and open data
• visualisation technologies (Tableau, PowerMap, QGIS, CartoDB)
• web visualisation (HTML5)

All content is based around real-world business examples.

Mathematics can be usefully applied to a wide range of applications in medicine and biology. Without assuming any prior biological knowledge, this module describes how mathematics helps us understand topics such as population dynamics, biological oscillations, pattern formation and nonlinear growth phenomena. There is considerable emphasis on model building and development.

This module will help develop skills in applying mathematical modelling to practical problems in biology and medicine. You will learn to apply a variety of mathematical and computational modelling approaches to a range of biomedical problems, including:

• modelling and analysis of biomedical systems using Ordinary Differential Equations
• phase-line and phase-plane analysis of models with one and two variables, with corresponding computational analysis
• stochastic models and simulation using the next-reaction method, and comparisons with equivalent differential equation models
• fitting models to data
• modelling spatial systems using Partial Differential Equations and individual-based models

This module will look at developing the concepts of frequentist and classical statistical inference. You will also learn to consider parameter estimation and the properties of parameters from both a mathematical and computational perspective.

Topics covered include maximum likelihood estimation, confidence intervals and likelihood ratio tests. There is an emphasis on the exponential family of distributions, which includes many standard distributions such as the normal, Poisson, binomial and gamma.

You will also explore the role of computers in performing statistical inference for non-standard (i.e. analytically intractable) problems. You’ll be introduced to optimisation methods, the bootstrap algorithm and simulation techniques including Monte Carlo methods in relation to problems of statistical inference.

Modelling is a fundamental part of statistics, enabling us to analyse and interpret data to understand the world and make predictions.

This module studies extensions of statistical modelling beyond the linear model, including non-linear and non-parametric regression and generalised linear models (GLMs) for binary and count data. These topics are the foundations of statistical machine learning.

You will gain an understanding of the theoretical foundations of these areas along with the knowledge of how to implement the techniques in a computationally efficient manner to analyse data.

In this module a variety of techniques and areas of mathematical optimization will be covered. You will study topics such as lagrangian methods for optimization, linear programming including the simplex algorithm, dynamic programming both deterministic control problems and stochastic problems. You will also cover network and graph algorithms.

During the module you will gain a rigorous mathematical background and develop the techniques for application through computational examples.

The first part of the module introduces no-arbitrage pricing principle and financial instruments such as forward and futures contracts, bonds and swaps, and options. The second part of the module considers the pricing and hedging of options and discrete-time discrete-space stochastic processes. The final part of the module focuses on the Black-Scholes formula for pricing European options and also introduces the Wiener process. Ito integrals and stochastic differential equations.

An in-depth look at specialised analytical techniques which present significant opportunities within business environments to extract actionable insights. Applications covered include Recommender Systems (for example, collaborative filtering in business), Text Analytics (linguistic processing, social media analysis), Spatial/Temporal analytics (for example, financial time series), Network analytics (for example, social graph analysis) and High dimensional analytics.

This module builds on Foundational Business Analytics covering more advanced predictive models and their motivation within business use cases. Students will establish knowledge of state-of-the-art prediction techniques including SVMs, temporal Nearest Neighbour models, Bayesian methods, Ensembles and Deep Learning.

Practical exercises will be set against a range of real world datasets and time series data. Focusing on the applicability of models to real world problems the module will consider the appropriateness and utility of each method with respect to common ''tricky'' data properties in real world data that lead to under-performing models.

Examples include unbalanced classes, heterogeneous input feature types and detrimentally large number of input features. Within the module methods to unpack the various predictive models to understand why they predict what they do and the utility of this information in various business contexts will be covered.

This module is taught primarily using Python against a background of industrial workflow data modelling environments (for example, SPSS Modeller, Orange) where applicable.

This module will help broaden your knowledge of statistics by introducing important contemporary topics in multivariate analysis. The focus is on application and high-level understanding, as well as light coverage of the underpinning mathematics behind each method.

You will cover key topics including:

• vector and matrix algebra ideas relevant to multivariate statistics, including the eigen and singular value decompositions
• methods for dimension reduction including principal components analysis, canonical correlation analysis and factor analysis
• multivariate regression methods
• classification methods, such as linear discriminant analysis
• multivariate normal distributions and their use in multivariate analysis of variance tests
• exploratory data analysis methods such as clustering tools, and multi-dimensional scaling, as well as other data visualisation techniques
• statistical software for conducting analysis of multivariate data

This module complements the frequentist statistical approach studied in the Advanced Statistical Inference module.

Bayesian inference has established itself as a popular alternative to traditional frequentist methods – and some of its techniques and ideas have found their way into many modern machine learning algorithms.

You will be introduced to the core concepts of the prior and posterior distributions of the parameters that underpin Bayesian statistics, covering the fundamental topics of prior elicitation, model conjugacy, predictive inference and model choice.

You will also study Markov Chain Monte Carlo (MCMC) and its implementation using statistical software, exploring a range of challenging modelling scenarios such as state-space models, dynamic linear models, mixed models and hierarchical models.

This module covers topics at the intersection between statistics and computer science, such as models that can adapt to and make predictions based on data.

It builds on the principles of statistical inference and linear regression to introduce neural networks as an advanced regression and classification tool. You will learn about bias-variance trade-off and methods to measure and compensate for overfitting, and their applications to AI.

The hands-on learning method using computing to study neural networks will help you apply them in tackling real-world challenges.

This module will cover several commonly occurring time series (temporal) models and their derived properties. You will learn methods for model identification for real-time series data and you’ll develop techniques for estimating the parameters of a model, assessing its fit and forecasting future values.

You will also learn methodology for spatial data, such as random fields and point processes, as well as inference for spatial data and interpolation for estimation. Throughout the module, computational methods will play an important role in implementing the methods of inference and prediction.

On this module, you will gain an understanding and practical experience of the predominant mathematical modelling and statistical inference approaches used in industrial pharmaceutical and chemical development.

You’ll cover topics including:

• Pharmacokinetics and Pharmacodynamics (PK-PD) modelling
• identifiability, sensitivity and model selection for PK-PD models
• statistical nonlinear mixed effects (NLME) modelling to account for patient variability when fitting data
• advanced partial differential equation models for space- and time-dependent drug delivery
• communicating the assumptions and outcomes of the modelling process with presentation of uncertainties

This module covers the advanced application of mathematical modelling and analysis to practical problems in biology, medicine and the life sciences, introducing you to published research and in the context of the widespread adoption of artificial intelligence and machine learning.

Through workshops and group activities, you will learn to tackle real-world challenges that professional mathematicians and systems biologists encounter.

During this module four major topics for the computational solution of problems in applied mathematics are considered.

• approximation theory
• numerical solution of nonlinear problems
• numerical solution of ODEs
• numerical solution of PDEs.

The focus is on formulating and understanding computational techniques with illustrations on elementary models from a variety of scientific applications. Specific contents include: approximation theory, multivariate polynomial approximation, Gauss quadrature, splines, trigonometric polynomials, DFTs, FFTs; numerical solution of (systems of) nonlinear equations; numerical differentiation and numerical solution of ODEs; introduction to PDEs and finite difference methods including error analysis. AI based coding assistants and state-of-the-art ML libraries for numerical analysis.