Advanced Computational Statistics and Data Analysis
MODULE CODE
CREDIT VALUE
DELIVERY
Module Aims
Aim 1
This module introduces advanced computational techniques for statistical analysis. Topics include simulation methods for discrete and continuous random variables, resampling methods such as jackknife and bootstrap, Monte Carlo techniques for statistical inference, categorical data analysis, and key Machine Learning algorithms for predictive modelling. Emphasis is placed on practical implementation using efficient computational techniques in R, enhancing students' proficiency in statistical computing.
Module Content
Discrete and Continuous Distributions: Basic properties of key discrete and continuous probability distributions.
Simulation: Simulation of Discrete and Continuous random variables, Inverse transformation method, Rejection Sampling, Monte Carlo Simulation, Monte Carlo Integration.
Resampling Techniques: Jackknife Method, Bootstrap Method.
Data Analysis: Description of data, graphical analysis, non-parametric estimation of the pdf
Machine Learning (ML): Study and application of various ML algorithms, including case studies
- Supervised Learning – e.g. Logistic Regression (binary, ordered, nominal), Classification, Decision Trees, Random Forests, Neural Networks, non- parametric regression
- Unsupervised Learning – e.g. Clustering (k-means, hierarchical clustering),
- Dimensionality reduction – e.g. Principal Component Analysis Categorical Data Analysis
Learning Outcomes
On successful completion of this module, a student will be able to:
Teaching Methods
The module will be delivered on campus, with weekly lecture and tutorial sessions.
Printed notes will be given ahead of time for each section of the course, to support and enhance students’ preparation and engagement during class sessions. Lectures will follow the notes, with discussions of the main theoretical topics, and study of examples of the applications of the theory. There will be a strong emphasis on student involvement in discussions in lectures, to encourage a more active approach to learning the material, and to allow the delivery to be tailored to build on the students’ current understanding. These will be complemented with sessions where students will use R or Python to work on their investigations.
Regular formative work in tutorial sessions will allow students to internalise the mathematical ideas and methods developed in the lectures, and lead to the development of problem-solving skills. This formative work will also feed back into the delivery of lectures and tutorials.
Assessment Methods
This module is assessed through a portfolio of exercises and a project.
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Compulsory
Optional
