Module MATH2801: Data Science & Statistical Modelling II

Department: Mathematical Sciences

MATH2801: Data Science & Statistical Modelling II

Prerequisites

• One of: Calculus I (Maths Hons) (MATH1081) OR Calculus I (MATH1061)
• AND
• one of: Linear Algebra I (Maths Hons) (MATH1091) OR Linear Algebra I (MATH1071)
• AND:
• Probability I (MATH1597)
• AND:
• Statistics I (MATH1617)

Corequisites

• Statistical Inference (MATH2XX1)

Excluded Combination of Modules

• None

Aims

• To equip students with the skills to import, explore, manipulate, visualise and report real data sets using the statistical programming language R.
• To introduce students to the concepts and mathematics behind sampling and sampling- based estimators.
• To provide a working knowledge of the theory, computation and practice of the linear model.

Content

• First half (Data Science):
• Modern usage of R: fundamentals of vectors, lists, data frames, data types, data visualization (base).
• Data wrangling: (tidy data with tidyr, data manipulation with dplyr, pipelines).
• Advanced graphics: ggplot2.
• Reporting tools and interactive dashboards: R Markdown, Shiny.
• Dates and strings.
• Monte Carlo hypothesis testing.
• Bootstrap resampling: parametric and non-parametric.
• Monte Carlo integration: approximating expectations, accuracy of approximation, sources of randomness.
• Generating random variables: inverse transform, rejection methods, importance sam-pling, discrete.
• Second half (Statistical Modelling)
• Review / introduction: multivariate normal distribution, Mahalanobis distance.
• Linear models: Estimation, inference and prediction.
• Factors, analysis of variance (ANOVA): full and partial F-tests, sequential ANOVA.
• Model selection: Akaike information criterion (AIC), Mallows’s statistic (Cp).
• Diagnostics & Transformations: residuals, influence, Cook’s distance, Box-Cox transformation.

Learning Outcomes

• By the end of the module students will:
• Have a solid foundation in the R programming language;
• Be able to import and manipulate real world data sets using modern libraries in the R ecosystem;
• Be able to perform an exploratory data analysis including a variety of visualisations;
• Understand the mathematics (methodology and theory) of sampling-based estimators and simple Monte Carlo simulation;
• Be able to use simulation approaches and apply the mathematics of sampling-based estimators to real world statistics problems.
• Be able to formulate a given problem in terms of the linear model and use the acquired skills to solve it;
• Have developed a set of skills to assess the suitability of a given linear model, and to compare it with competing models;
• Have a systematic and coherent understanding of the theory and mathematics underlying the statistical methods studied;
• Be able to relate the conceptual framework to practical implementations of the methods;
• Have acquired a coherent body of knowledge on regression methodology, based on which extensions of the linear model such as generalized models or nonparametric regression can be learnt and understood.

• Students will have foundational skills in data science, specifically in data import, manipulation and exploration.
• Students will have basic mathematical and statistical skills in the following areas: modelling, computation, simulation and sampling-based methodology.

• Students will have basic skills in the following: synthesis of data, critical and analytical thinking, computer skills.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
• Problem classes show how to solve example problems in an ideal way, revealing also the thought processes behind such solutions.
• Tutorials provide active problem-solving engagement and immediate feedback to the learning process.
• Practicals consolidate the studied material, explore theoretical ideas in practice, enhance practical understanding, and develop practical data analysis skills.
• Formative assessments provide feedback to guide students in the correct development of their knowledge and skills in preparation for the summative assessment.
• Computer-based examinations assess the ability to use statistical software and basic programming to solve predictable and unpredictable problems.
• The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Fortnightly assignments

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University