My fourth year Statistics modules described for A-Level students
Right now I am in the midst of exams. Having spent 2 years on OurWarwick, I realise now I have never described my modules as a statistician.
Modules certainly change over the years and so you cannot assume that the modules you take in the future will be identical to mine. However, the majority of my modules focus upon the key foundations any statistician would need during their career. In this post I cut through the jargon and explain my modules in a nutshell.
Bayesian Statistics is a field of research which the University of Warwick is particularly renowned for. This work explores applications of Bayes Theorem, a theorem you definitely see within any Statistics module in A-Level Maths:
This is an incredibly powerful theorem you will see everywhere at university. Within Bayesian statistics modules we can think of A as some event we want to predict and B some useful information we want to use to predict A. Bayesian statistics helps us make reasonable predictions for some observation if we make some assumptions on parameters we think are behind observations. This forms the basis of my module Bayesian Forecasting and Intervention.
We can also use Bayesian statistics to determine which decision is best if we are given a game, such as betting on either Ukraine or the UK to win the Eurovision song contest. This application of Bayes rule, to maximise your reward within betting games, is discussed in Bayesian Statistics and Decision Theory. In this module we also use Directed Acyclic Graphs to determine which variables are relevant and irrelevant in predicting outcomes. For example we can consider how factors such as: the time you get out of bed, the weather, and your choice of breakfast impact on the time you arrive at university.
Within Medical statistics we consider how statistics can be used to determine the effectiveness of trial treatment and general trial methodology. We use non-parametric methods (ie. just using the data), and parametric methods (using the data alongside additional model assumptions) to predict the survival of patients given certain treatments. These techniques use models previously studied in other modules (such as generalised linear models) alongside models unique to medical statistics (such as Kaplan-Meier curves).
Applied Stochastic Processes
Whatever university you study at, I am confident you will come across stochastic processes. Stochastic processes can be thought of as a collection of random variables which we use to model mathematical processes (such as predicting COVID infection levels) which often vary in a random way. In this module we consider Markov Processes. Imagine you are on stepping stones and you flip a coin to decide to jump either to the left or right stone. The only information I need in order to predict your next step is your current location, not where you have been. We consider this Markov property within this module to predict how long you’ll be in the Tesco self-checkout queue in rush hour, the likelihood of an infection becoming a pandemic and how many house insurance claims an insurance company will receive every hour.
Monte Carlo Methods
Monte Carlo methods focusses upon sampling from distributions which are hard to sample from. For example, suppose you want to sample from a Normal distribution with mean 1 and variance 0, how can you make sure that if you plotted the frequency of samples it would have the normal distribution bell shape?
Monte Carlo methods help us to sample from difficult distributions using distributions which we can sample from.
Statistical Learning and Big Data
This module covered the most significant statistical discoveries utilised right now to fit statistical models. Big data is becoming more and more prevalent within our society as storing vast amounts of data becomes easier. This module gave a run through of the statistical methodology currently available which we can use to build artificial intelligence.
AI sounded mystical to me at the start of the module but it is in fact deep-rooted in statistical research. This module introduced me to neural networks, classification methods and new Monte Carlo algorithms.
When you’re fundraising, it’s AI
When you’re hiring, it’s ML
When you’re implementing, it’s linear regression
I hope you found this an accessible run-down of my fourth year modules, if you have any comments or questions feel free to either comment on my blog or IM me on OurWarwick!