MSC AI & DATA SCIENCE / MODULE 03

Advanced Statistical & Mathematical Methods

Linear algebra, statistical inference and the assumptions behind model evaluation.

THE PRACTICE BEHIND THE MODULE

What I take into the work

Mathematics helps me explain what a result can support. A significant test is a prompt for closer investigation, not a causal account on its own.

Linear algebra, statistical inference and the assumptions behind model evaluation.

FROM THE SOURCE REFLECTION

Course reflection

My account of the learning and its application, distilled from my combined course reflection. The original document is held privately.

Vectors, transformations and systems of equations built the mathematical language for data representation and model behaviour.
Descriptive and inferential statistics added uncertainty, confidence intervals, hypothesis testing and experimental design to the question of what a result means.
I applied ANOVA to restricted planning data to examine variation across project categories. The test invites contextual investigation; it does not establish why the difference arose.

About the code: Python code and notebooks for the coded studies are privately stored and maintained by me. I’m happy to answer questions about the methods and their limits; any sharing of an artefact would depend on the permissions and data involved.

MILESTONES IN PRACTICE

From method to judgment

Three steps show how the learning moved into an artefact or decision, and where the evidence stops.

Calculate

Work through vector operations and visualise the geometry with Python.

Test

Use ANOVA on restricted resource-planning data to examine category differences.

Qualify

Check assumptions and distinguish statistical difference from its organisational cause.

SELECTED PORTFOLIO EVIDENCE

Applied studies

Original summaries of my work. Each distinguishes the source, the work's stage and what it can support.

APPLIED STUDY

Vectors and geometric reasoning

Data basis: Illustrative numerical examples
Stage: Completed problem-solving study

I worked through vector operations and Python visualisations to connect manual calculations with the geometry used in data science and machine learning.

Reading the evidence
The examples develop mathematical fluency; they are not operational data or a workplace result.

APPLIED STUDY

Patterns in resource allocation

Data basis: Restricted, real workplace planning data
Stage: Completed academic analysis; no live decision tool

I framed a question about whether business analyst allocation differed across project categories, then used analysis of variance and a Python check to examine the data.

Reading the evidence
The observed difference belongs to that source and its assumptions. Project type alone does not explain why allocations differ or justify a staffing intervention.

EVIDENCE & PRIVACY

These summaries do not reproduce academic submissions, restricted datasets, individual records, internal systems detail or private course materials. A design, prototype and deployed service are different stages; each study is labelled accordingly.

A CLOSER LOOK

Compare predictions with held-out values. Original academic output from the synthetic student exercise. It illustrates error inspection, not a forecast for actual students. — Original academic output from the synthetic student exercise. It illustrates error inspection, not a forecast for actual students.

FOLLOW THE THREADNine-module map ↗Analytics study ↗Previous: Data Driven Analytics ↗Next: Stakeholders, Negotiation & Project Management ↗

Watch my QMUL apprenticeship interview and read the learning reflection — the personal journey behind these methods.

EXPLAINABLE AI & DATA / READ THE METHOD

Connect the learning to the evidence.

Use the categories to distinguish a capability, an algorithm, a Python package and a delivery step. A mention in a module or case study does not mean that capability is running on this page.

Follow the reasoning.

QuestionChoose the decision to support
MethodMatch the task to a suitable approach
TestCompare with appropriate evidence
ExplainState limits and human responsibility

Explore the building blocks.

AI Capability4

AI/Data Concepts1

Data Science Pipeline1

Evaluation & XAI2

Python Package3

Responsible AI1

Number of concepts in this guide, not performance or usage measures.

Explore the explanation matrix · 12 concepts

Concept categoryFind a term or example

12 concepts shown

On small screens, scroll the table sideways. “Learning context” explains a related idea; it does not mean that method runs on this page. Deep learning is the standard term for “deep ML”.

Technical term	Technical description / definition	In plain English	How this page uses it
Machine learning (ML)AI Capability	Methods that estimate patterns or parameters from examples to support inference on other inputs.Primary reference ↗	Learn a pattern from examples, then check whether it helps with new ones.	Learning context ML learns from examples. Read the page-specific methods below to see whether any model runs here.
Deep learningAI Capability	Machine learning using neural networks with multiple representation-learning layers.Primary reference ↗	A layered model learns useful representations; more layers do not guarantee a better answer.	Learning context Deep learning is an AI capability, not a label for every chart. No deep model is implied by this explanation panel.
Natural language processing (NLP)AI Capability	Computational methods for representing, analysing or generating human language.Primary reference ↗	Help a computer work with words, while remembering that context matters.	Learning context Text search, translation, thematic classification and generation are different language tasks; their implementation is identified separately.
Sentiment analysisAI Capability	A language-analysis task that estimates an expressed attitude, often as polarity or sentiment categories.Primary reference ↗	Estimate the tone of words—not the private feelings or personality of their author.	Learning context Sentiment estimates expressed tone. It must not be confused with topic classification or a diagnosis of a person.
Data science pipelineData Science Pipeline	An ordered, reproducible sequence for acquiring, validating, preparing, analysing and evaluating data.Primary reference ↗	A chain from a question and source to an answer someone can check.	Method guide The learning-to-practice path connects framing, preparation, modelling, evaluation and communication.
Features and labelsAI/Data Concepts	Features are model inputs; labels are target values or categories used in supervised learning.Primary reference ↗	What the model sees, and the answer it is learning to estimate.	Learning context Projects define relevant input features and any target labels before choosing an estimator.
Held-out evaluationEvaluation & XAI	Assessment on examples excluded from fitting and model selection, according to the declared split.Primary reference ↗	Keep some answers out of practice so the test means something.	Learning context Unseen and appropriately separated cases help assess whether a learned pattern generalises.
Explanation versus causal proofEvaluation & XAI	A model explanation describes selected behaviour or contributions; it does not establish causal effects or full reliability.Primary reference ↗	A reason for this output is useful, but it is not proof that the model is right.	Responsible use Explain what was actually done and what the available evidence supports.
NumPyPython Package	A Python library for multidimensional arrays and numerical operations.Primary reference ↗	The numerical toolbox behind many Python calculations.	Learning context A numerical Python library; it is not an AI capability or an algorithm by itself.
pandasPython Package	A Python library for labelled tabular data manipulation and analysis.Primary reference ↗	A programmable workbench for cleaning and comparing tables.	Learning context A tabular Python library; a useful preparation tool, not a prediction model.
scikit-learnPython Package	A Python library providing estimators, preprocessing tools and model-evaluation utilities.Primary reference ↗	A toolkit of models and fairer ways to test them.	Learning context A Python library of algorithms and evaluation tools, distinct from each fitted model.
Human oversight and consentResponsible AI	People retain appropriate review authority, permission controls and correction routes for data use and outputs.Primary reference ↗	Keep someone able to question, correct or stop the result.	Responsible use Decision ownership, permission and correction belong throughout the workflow.