# Studying Probability and Statistics

Probability and Statistics spans a range from pure mathematical analysis, through the modelling of random processes, to heavily computational applied statistics such as data mining. It is of interest both as an academic subject and because of its immense importance in applications. Many of the careers followed by mathematical sciences graduates involve probabilistic modelling or sophisticated data analysis. In fact, Hal Varian, Google’s Chief Economist has recently said, "I keep saying the sexy job in the next ten years will be to be a statistician." See Dream job of the next decade. A graph showing how part of the blogosphere is connected. Modelling and analysing these sort of random structures has become an important part of modern Statistics.

Warwick's research group in probability and statistics is one of the largest in Britain. Its staff and its lecture courses are spread between the Mathematics and Statistics Departments. Here is how to get the best out of what is available.

Course structure

Year 1.

Higher level modules build on the linear algebra, analysis and probability studied in first year. Note that the optional second half of ST111/2 Probability A and B is a prerequisite for most of the higher level probability and statistics courses.

Statistical Laboratory is an optional module where you can gain experience of simulation and data analysis with the widely used statistical programming language R. Note that several later Stats modules will assume that students know how to use R. In particular ST323 Multivariable Calculus coursework requires it to do meaningful analysis on data sets.

Year 2.

If you want to have the option of taking third year Statistics modules, then it is important to take Introduction to Mathematical Statistics. In this module you study statistical inference, the process of drawing conclusions from data that is subject to random variation, and the mathematics it is based upon.

The module and Stochastic processes introduces the Markov property and its use in building probabilistic models for diverse applications such as random networks, population growth, queues and epidemics.

Year 3 and beyond....

Third year Statistics modules cover a wide range of methods and applications showing how mathematics can be used to extract information from data and make decisions. These modules include Multivariate Statistics, Bayesian Statistics, Medical Statistics, Designed Experiments, and Bayesian Forecasting and Intervention.

In the modules Random discrete Structures, Markov processes and Percolation Theory and Applied Stochastic Processes you can study various more sophisticated mathematical models for random structures and processes that are both intrinsically interesting mathematical objects and also very important for applications. A "flash crash" caused by high frequency trading on the stock market. Hedge funds make extensive use of probability theory to decide when to buy and sell financial contracts. The basic principles are covered in module Introduction to Mathematical Finance.

Advanced probability requires a mathematical framework called measure theory developed by some of the greatest mathematicians of the twentieth century (Borel, Kolmogorov, and Wiener...) It is taught at Warwick in Probability Theory and Measure Theory. Often students who are strong in analysis find that they enjoy studying measure-theoretic probability. This leads to advanced modules such as Brownian Motion and Stochastic Analysis. These are useful for students who wish to work as financial analysts in the City, work in scientific research and development, or who are considering continuing on to do a PhD in Mathematics or Statistics.