MATH2801: Data Science & Statistical Modelling II

• 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)

• Statistical Inference (MATH2761)

• None

• 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.

• 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 sampling, 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), Mallowss statistic (Cp).
• Diagnostics & Transformations: residuals, influence, Cooks distance, Box-Cox transformation.

Subject-specific Knowledge:

• 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.

Subject-specific Skills:

• 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.

Key Skills:

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

• 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.

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